# Solve for x: (x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6 - Mathematics

Solve for x: (x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6

#### Solution

Solution:

(x-3)/(x-4)+(x-5)/(x-6)=10/3

[(x-3)(x-6)+(x-5)(x-4)]/((x-4)(x-6))=10/3

(x^2-9x+18+x^2-9x+20)/((x-4)(x-6))=10/3

(2x^2-18x+38)/((x-4)(x-6))=10/3

(2(x62-9x+19))/x=10/3(x^2-10x+24)

(x-9x+19)/1=5/3[x^2-10x+24]

3x^2-27x+57=5x^2-50x+120

2x^2-23x+63=0

x=7 or x=9/2

Concept: Solutions of Quadratic Equations by Factorization
Is there an error in this question or solution?