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Simplification Of Algebraic Expression

Class 8th Mathematics West Bengal Board Solution
Lets Do 15.1
  1. {a+b}/{c} = frac {a}/{c} + frac {b}/{c} Lt’s see the relations below and find which…
  2. {2x}/{3ab} - frac {3b}/{6ac} Let's simplify:
  3. {a}/{x+y} = frac {a}/{x} + frac {a}/{y} Lt’s see the relations below and find which…
  4. {4xy}/{3mn} - frac {2yz}/{6n} Let's simplify:
  5. {x-y}/{a-b} = frac {y-x}/{b-a} Lt’s see the relations below and find which one is true…
  6. {a}/{ a^{2} + ab } - frac {b}/{ (a+b)^{2} } Let's simplify:
  7. {1}/{x} + frac {1}/{y} = frac {1}/{x+y} Lt’s see the relations below and find which…
  8. {x}/{ x^{2} + xy } - frac {x}/{x-y} Let's simplify:
  9. { 63a^{3}b^{4} }/{ 77b^{5} } Let’s express the following algebraic fractions in the…
  10. { 18a^{4}b^{5}c^{2} }/{ 21a^{7}b^{2} } Let’s express the following algebraic fractions…
  11. { x^{2} - 3x+2 }/{ x^{2} - 1 } Let’s express the following algebraic fractions in the…
  12. {a+1}/{a-2} x frac { a^{2} - a-2 }/{ a^{2} + a } Let’s express the following…
  13. { p^{3} + q^{3} }/{ p^{2} - q^{2} } / frac {p+q}/{p-q} Let’s express the following…
  14. { x^{2} - x-6 }/{ x^{2} + 4x-5 } x frac { x^{2} + 6x+5 }/{ x^{2} - 4x+3 } Let’s…
  15. { a^{2} - ab+b^{2} }/{ a^{2} + ab } / frac { a^{3} + b^{3} }/{ a^{2} - b^{2} }…
  16. {1}/{ab} + frac {1}/{bc} + frac {1}/{ca} Let’s simplify the following algebraic…
  17. {a-b-c}/{a} + frac {a+b+c}/{a} Let’s simplify the following algebraic expressions.…
  18. { x^{2} + a^{2} }/{ab} + frac {x-a}/{ax} - frac { x^{3} }/{b} Let’s simplify the…
  19. {2a^{2}b}/{3b^{2}c} x frac { c^{4} }/{ 3a^{3} } / frac { 4bc^{3} }/{ 9a^{2} }…
  20. {1}/{ x^{2} - 3x+2 } + frac {1}/{ x^{2} - 5x+6 } + frac {1}/{ x^{2} - 4x+3 } Let’s…
  21. {1}/{x-1} + frac {1}/{x+1} + frac {2x}/{ x^{2} + 1 } + frac { 4x^{3} }/{ x^{4} + 1 }…
  22. { b^{2} - 5b }/{3b-4a} x frac { 9b^{2} - 16a^{2} }/{ b^{2} - 25 } / frac { 3b^{2}…
  23. {b+c}/{ (a-b) (a-c) } + frac {c+a}/{ (b-a) (b-c) } + frac {a+b}/{ (c-a) (c-b) } Let’s…
  24. {b+c-a}/{ (a-b) (a-c) } + frac {c+a-b}/{ (b-a) (b-c) } + frac {a+b-c}/{ (c-a) (c-b) }…
  25. { frac { a^{2} }/{x-a} + frac { b^{2} }/{x-b} + frac { c^{2} }/{x-c}+a+b+c }/{ frac…
  26. ( { a^{2} + b^{2} }/{ a^{2} - b^{2} } - frac { a^{2} - b^{2} }/{ a^{2} + b^{2} } )…
  27. {b+c}/{bc} (b+c-a) + frac {c+a}/{ca} (c+a-b) + frac {a+b}/{ab} (a+b-c) Let’s simplify…
  28. { y^{2} + yz+z^{2} }/{ (x-y) (x-z) } + frac { z^{2} + zx+x^{2} }/{ (y-z) (y-x) } +…
Lets Do 15.2
  1. Lets express in reduced from: { a (a+b) }/{a-b} x frac {a-b}/{ b (a+b) } times…
Lets Do 15.3
  1. { a^{2} x c^{2} }/{ c^{2} times d^{2} } / frac {bc}/{ad} Lets express the…
  2. { x^{2}y-xy^{2} }/{ x^{2} - xy } Lets express the algebraic expression given below in…
  3. { p^{2} - q^{2} }/{x+y} / frac {p-q}/{ x^{2} - y^{2} } Lets express the algebraic…
Lets Do 15.1
Question 1.

Lt’s see the relations below and find which one is true and which one is false:
Answer:

Consider LHS,



= RHS


So, the given relation is true.
Question 2.

Let's simplify:
Answer:

Given


Multiply and divide the first part with ‘2c’, and the second part with ‘3b’, we get





Hence



Question 3.

Lt’s see the relations below and find which one is true and which one is false:
Answer:


So, the given statement is false.
Question 4.

Let's simplify:
Answer:

Given



Multiply and divide the second part with ‘m’, we get





Hence



Question 5.

Lt’s see the relations below and find which one is true and which one is false:
Answer:

Consider LHS,



Multiplying and dividing by (-1), we get,



= RHS


So, the given relation is true.
Question 6.

Let's simplify:
Answer:

Given




Multiply and divide the first part with ‘(a + b)’, we get






We can (a + b)2 in simplified form as (a + b)2 = a2 + 2ab + b2, we get


Or


Hence



Question 7.

Lt’s see the relations below and find which one is true and which one is false:
Answer:

(iv)


Consider LHS,




So, the given relation is false.
Question 8.

Let's simplify:
Answer:

Given




Multiply and divide the first part with ‘(x - y)’ and the second part with ‘(x + y)’, we get





But we know (x + y)(x - y) = (x2 - y2), so the above expression becomes,




Hence



Question 9.

Let’s express the following algebraic fractions in the reduced from:
Answer:


Cancelling 7b4, we get,
Question 10.

Let’s express the following algebraic fractions in the reduced from:
Answer:


Cancelling 3a4b2, we get,
Question 11.

Let’s express the following algebraic fractions in the reduced from:
Answer:







Question 12.

Let’s express the following algebraic fractions in the reduced from:
Answer:

(iv)





Cancelling same terms from numerator and denominator.
Question 13.

Let’s express the following algebraic fractions in the reduced from:
Answer:



Cancelling same terms from numerator and denominator.
Question 14.

Let’s express the following algebraic fractions in the reduced from:
Answer:





Cancelling same terms from numerator and denominator, we get
Question 15.

Let’s express the following algebraic fractions in the reduced from:
Answer:




Cancelling same terms from numerator and denominator, we get
Question 16.

Let’s simplify the following algebraic expressions.
Answer:


Multiplying and dividing first term by c, second term by a and third term by b respectively, we get,
Question 17.

Let’s simplify the following algebraic expressions.
Answer:







Question 18.

Let’s simplify the following algebraic expressions.
Answer:






Question 19.

Let’s simplify the following algebraic expressions.
Answer:




Cancelling same terms from numerator and denominator we get,
Question 20.

Let’s simplify the following algebraic expressions.
Answer:





Multiplying first term by (x – 3), second term by (x – 1), third term by (x – 2), respectively, we get,
Question 21.

Let’s simplify the following algebraic expressions.
Answer:











Question 22.

Let’s simplify the following algebraic expressions.
Answer:




Cancelling same terms from denominator we get,


= a
Question 23.

Let’s simplify the following algebraic expressions.
Answer:


Multiplying and dividing all three terms with (-1).


Also, multiplying and dividing first term with (b – c), second term with (c – a), third term with (a – b).






= 0
Question 24.

Let’s simplify the following algebraic expressions.
Answer:


Multiplying and dividing all three terms with (-1).


Also, multiplying and dividing first term with (b – c), second term with (c – a), third term with (a – b).






= 0
Question 25.

Let’s simplify the following algebraic expressions.
Answer:





= x
Question 26.

Let’s simplify the following algebraic expressions.
Answer:











= 1
Question 27.

Let’s simplify the following algebraic expressions.
Answer:




Multiplying and dividing first term by a, second term by b and third term by c, we get







= 6
Question 28.

Let’s simplify the following algebraic expressions.
Answer:


Multiplying and dividing all three terms with (-1).


Also, multiplying and dividing first term with (y – z), second term with (z – x), third term with (x – y).






= 0
Lets Do 15.2
Question 1.

Lets express in reduced from:


Answer:

Given



Cancelling the like terms, we get




Cancelling the like terms, we get



Combining the like terms, we get



Hence the given expression in reduced form is as shown below,
Lets Do 15.3
Question 1.

Lets express the algebraic expression given below in reduced from:
Answer:

Given


By cancelling the like term ‘c2’, we get



But we know, , so the above expression becomes



By cancelling the like terms, we get




Hence



Question 2.

Lets express the algebraic expression given below in reduced from:
Answer:

Given


Bringing out the common variable out, we get



Now cancelling the like terms, we get



Hence



Question 3.

Lets express the algebraic expression given below in reduced from:
Answer:

Given



But we know, , so the above expression becomes



But we know (x2 - y2) = (x + y)(x - y), so the above expression becomes,



Now cancelling the like terms, we get


⇒ = (p + q)(x - y)


By opening the brackets, we get


⇒ = p(x - y) + q(x - y)


⇒ = px - py + qx - qy


Hence