Question

x/b-b = x/a-a solve for x

Answer 1

ANSWER:

Given:

• (x/b) - b = (x/a) - a

To Find:

• Value of x

Solution:

$\text{We are given that,}\\\\:\longrightarrow\dfrac{x}{b}-b=\dfrac{x}{a}-a\\\\:\implies\dfrac{x-b^2}{b}=\dfrac{x-a^2}{a}\\\\\text{On cross-multiplying,}\\\\:\implies a(x-b^2)=b(x-a^2)\\\\:\implies ax-ab^2=bx-a^2b$

$\text{On rearranging the terms,}\\\\:\implies ax-bx=ab^2-a^2b\\\\:\implies x(a-b)=ab(b-a)\\\\:\implies x(a-b)=-ab(a-b)\\\\\text{On canceling (a - b),}\\\\\bf{:\implies x=-ab}\\\\\text{\bf{Value of x is -ab}}$