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

1 Answer
Jun 28, 2016

Answer:

#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)|)))#