# How do you solve the rational equation 40/(b-19)=-17/(b+1)?

Jun 28, 2016

$b = \frac{283}{57}$

#### Explanation:

Given,

$\frac{40}{b - 19} = - \frac{17}{b + 1}$

Multiply both sides by the product of the denominators which are on either side of the equation.

$\left(b - 19\right) \left(b + 1\right) \left(\frac{40}{b - 19}\right) = \left(b - 19\right) \left(b + 1\right) \left(- \frac{17}{b + 1}\right)$

The common factors which appear in the numerator and denominator cancel each other out.

$\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{b - 19}}}\right) \left(b + 1\right) \left(\frac{40}{\textcolor{red}{\cancel{\textcolor{b l a c k}{b - 19}}}}\right) = \left(b - 19\right) \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{b + 1}}}\right) \left(- \frac{17}{\textcolor{red}{\cancel{\textcolor{b l a c k}{b + 1}}}}\right)$

$40 \left(b + 1\right) = - 17 \left(b - 19\right)$

Expand.

$40 b + 40 = - 17 b + 323$

Bring all terms with $b$ to the left side and the terms without a $b$ to the right.

$40 b + 17 b = 323 - 40$

Simplifying,

$57 b = 283$

$b = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{283}{57}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$