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

1 Answer
Jun 28, 2016

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)|)))