How do you solve for x in  \frac { 9} { w + 8} = \frac { x } { ( w - 7) ( w + 8) }?

Nov 15, 2017

$\implies x = 9 w - 63$

Explanation:

$\setminus \frac{9}{w + 8} = \setminus \frac{x}{\left(w - 7\right) \left(w + 8\right)}$

By transposition:

$\implies 9 = \setminus \frac{x \left(w + 8\right)}{\left(w - 7\right) \left(w + 8\right)}$

$\implies 9 = \setminus \frac{x \cancel{\left(w + 8\right)}}{\left(w - 7\right) \cancel{w + 8}}$

$\implies 9 = \setminus \frac{x}{\left(w - 7\right)}$

$\implies 9 \left(w - 7\right) = x$

$\implies 9 w - 63 = x$

$\implies x = 9 w - 63$

Nov 15, 2017

$x = 9 \left(w - 7\right)$

Explanation:

Start by cancelling $w + 8$ from both sides of the equation

$\frac{9}{\cancel{w + 8}} = \frac{x}{\left(w - 7\right) \cancel{\left(w + 8\right)}}$

$9 = \frac{x}{w - 7}$

Multiply both sides by $w - 7$, cancelling it on the right.

$9 \textcolor{red}{\left(w - 7\right)} = \frac{x}{\cancel{w - 7}} \cancel{\textcolor{red}{\left(w - 7\right)}}$

$9 \left(w - 7\right) = x$

Rewriting from left to right,

$x = 9 \left(w - 7\right)$