Answer
$x=\dfrac{7a^2+b^2}{4a-b}$
Work Step by Step
By cross-multiplication, in terms of $x$, the given equation, $ \dfrac{x+b}{a}=\dfrac{4x-7a}{b} ,$ is equivalent to \begin{array}{l}\require{cancel} b(x+b)=a(4x-7a) \\\\ bx+b^2=4ax-7a^2 \\\\ bx-4ax=-7a^2-b^2 \\\\ x(b-4a)=-7a^2-b^2 \\\\ x=\dfrac{-7a^2-b^2}{b-4a}
\\\\
x=\dfrac{-(7a^2+b^2)}{-(4a-b)}
\\\\
x=\dfrac{7a^2+b^2}{4a-b}
.\end{array}
