How do you solve (r+3)/(r-4) = (r-5)/(r+4)?

2 Answers
Jun 4, 2017

r=1/2

Explanation:

Eliminate the fractions by cross multiplying: (r+3)/(r-4)=(r-5)/(r+4) becomes (r+3)(r+4)=(r-5)(r-4)
Distribute each binomial to get two quadratic equations: r^2+7r+12=r^2-9r+20
Subtract r^2 from both sides: 7r+12=-9r+20
Add 9 to both sides: 16r+12=20
Subtract 12 from both sides: 16r=8
Divide both sides by 16: r=8/16
Simplify: r=1/2

To check your answer, plug in 1/2 to each equation and solve:
(1/2+3)/(1/2-4)=(1/2+5)/(1/2+4)
From there, just simplify: (7/2)/(-7/2)=(-9/2)/(9/2)
-1=-1

Jun 4, 2017

r= 1/2

Explanation:

First cross multiply to give you a linear equation.

(r+3)(r+4) = (r-4)(r-5)
r^2 + 7r + 12 = r^2 -9r + 20

Then make the equation equal zero.

(r^2 +7r+12)-(r^2 -9r+20) = 0

The r^2 cancel out leaving this equation:

16r - 8 = 0
16r = 8

r= 8/16 = 1/2