Question

Solve for $x$.

$\frac{x+3}{x-2}-\frac{1-x}{x}=4\frac{1}{4}$

Answer 1

Consider the given equation.

$\frac{x+3}{x-2}-\frac{1-x}{x}=4\frac{1}{4}$

$\frac{x^2+3x-x+x^2+2-2x}{x^2-2x}=\frac{17}{4}$

$4(2x^2+2)=17(x^2-2x)$

$8x^2+8=17x^2-34x$

$9x^2-34x-8=0$

$x=4,-\frac{2}{9}$

Hence, these are the required values of $x$.