Question

plZ ans the ques i will very thankful to u​

Answer 1

The answer is option (a) ab.

We can check it by taking any two numbers as example.

Let us check for a=6 and b=2.

a:b = 6:2 = 3:1

a²:b² = 36:4

Now, a²+ab : b²+ab = 36+12 : 4+12 = 48 : 16 = 3 : 1 = a:b

Hence option (a) is the answer.

Answer 2

Answer:

lets add 'x' to both the denominator and numerator

$\frac{a^{2}+x}{b^{2}+x} = \frac{a}{b} \\\\b(a^{2}+x) = a(b^{2}+x) \\\\ba^{2}+bx = ab^{2}+ax \\\\ba^{2}+bx - ab^{2}-ax = 0\\\\ab(a-b)-x(a-b) = 0\\\\(ab-x)(a-b)=0\\\\ab-x = 0 \\ \\x = ab\\\\option(a)$