# How do you solve (x-6/5)/x-(x-10 1/2)/(x-5)=(x+21)/(x^2-5x)?

Nov 5, 2017

$x = \frac{50}{11}$

#### Explanation:

Rewriting the right side of the equation,
The common denominator is ${x}^{2} - 5 x$

$\frac{\left(x - 5\right) \left(x - \frac{6}{5}\right)}{{x}^{2} - 5 x} - \frac{x \left(x - 10.5\right)}{{x}^{2} - 5 x} = \frac{x + 21}{{x}^{2} - 5 x}$

Multiplying both sides of the equation by ${x}^{2} - 5 x$,

$\left(x - 5\right) \left(x - \frac{6}{5}\right) - x \left(x - 10.5\right) = x + 21$

Simplifying further,
$\left({x}^{2} - \frac{31}{5} x + 6\right) - \left({x}^{2} - 10.5 x\right) = x + 21$
${x}^{2} - \frac{31}{5} x - {x}^{2} + 10.5 x - x = 21 - 6$
$- \frac{33}{10} x = 15$
$x = \frac{50}{11}$