How do you solve \frac { 5x + 1} { x - 1} = \frac { 15x - 17} { 3x - 7}?

1 Answer
May 12, 2018

no real solutions for x

Explanation:

(5x+1)/(x-1)=(15x-17)/(3x-7)

(5x+1)/(x-1)xx(x-1)(3x-7)=(15x-17)/(3x-7)xx(x-1)(3x-7)

(5x+1)xx(3x-7)=(15x-17)xx(3x-7)

5x(3x-7)+1(3x-7)=15x(3x-7)-17(3x-7)

15x^2-35x+3x-7=45x^2-105-51x+119

15x^2-32x-7=45x^2-51x+14

0=(45-15)x^2+(-51+32)x+(14+7)

0=30x^2-19x+21

find discriminant:
Delta=(-19)^2-4xx30xx21=-2159
Delta<0
:.no real solutions for x