Question

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

Answer 1

`b=283/57`

Explanation:

Given,

`40/(b-19)=-17/(b+1)`

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

`(b-19)(b+1)(40/(b-19))=(b-19)(b+1)(-17/(b+1))`

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

`(color(red)cancelcolor(black)(b-19))(b+1)(40/(color(red)cancelcolor(black)(b-19)))=(b-19)(color(red)cancelcolor(black)(b+1))(-17/(color(red)cancelcolor(black)(b+1)))`

`40(b+1)=-17(b-19)`

Expand.

`40b+40=-17b+323`

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

`40b+17b=323-40`

Simplifying,

`57b=283`

`b=color(green)(|bar(ul(color(white)(a/a)color(black)(283/57)color(white)(a/a)|)))`