Question

x/a-b = a/x-b then x = ?

A. b-a, -a B. b-a, 1/a
C. a-b, b^2 D. b-a, a

Answer 1

$\frac{x}{a - b} = \frac{a}{x - b}$
>x(x-b)=a(a-b)
>x²-xb-a(a-b)=0
>x²-xb-a²+ab=0
>x²-xb-a²+ab-xa+xa=0
>x²-xa-xb+xa+ab-a²=0
>x(x-a)-x(b-a)+a(b-a)=0
>x(x-a)-(b-a)(x-a)=0
>[x-(b-a)](x-a)=0
so X=b-a ; a
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