Question

Solve the following quadratic equations by factorization:

`(2x)/(x-4)+(2x-5)/(x-3)=25/3`

Answer 1

We have been given

`(2x)/(x-4)+(2x-5)/(x-3)=25/3`

`(2x(x-3)+(2x-5)(x-4))/(x^2-7x+12)=25/3`

6x² - 18x + 6x² - 24x - 15x + 60 = 25x² - 175x + 300

13x² - 118x + 240 = 0

13x² - 78x - 40x + 240 = 0

13x(x - 6) - 40(x - 6) = 0

(x - 6)(13x - 40) = 0

Therefore,

x - 6 = 0

x = 6

or,

13x - 40 = 0

13x = 40

x = 40/13

Hence, x = 6 or x = 40/13