{a²-b²+a(a+b)}{a(a-b)+b(a-b)},a≠b, is equal to

Correct Answer is : 2a−ba−b2a-b/a-ba−b2a−b

Correct Answer is : 2a−ba−b2a-b/a-ba−b2a−b

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CTET Paper II (Mathematics and Science) 1 Jan 2022 Solved Paper

Question : 42 of 150

Marks: +1, -0

\frac{a^{2}-b^{2}+a(a+b)}{a(a-b)+b(a-b)},a≠b

, is equal to

Solution:

Concept:

Use the identity

a^2 - b^2 = (a - b)(a + b)

and factor common terms to simplify the fraction.

Explanation:

Start with the given expression:

\frac{a^{2}-b^{2}+a(a+b)}{a(a-b)+b(a-b)}

Rewrite

a^{2}-b^{2}

(a-b)(a+b)

. The numerator becomes

(a-b)(a+b) + a(a+b)

Factor

(a+b)

from the numerator:

(a+b)[(a-b) + a] = (a+b)(2a-b)

In the denominator, factor

(a-b)

from both terms:

a(a-b)+b(a-b) = (a-b)(a+b)

Now the fraction is

\frac{(a+b)(2a-b)}{(a-b)(a+b)}

. Cancel

(a+b)

(since

a\neq b

, denominator is non‑zero).

Result:

\frac{2a-b}{a-b}

Answer:

Option C:

\frac{2a-b}{a-b}

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