122111 15 128T 15 I3 15 Solution2 x5 x2 2x 11 x2 8

Solution

{2 / ( x-5 )} ={ ( x^2 - 2x - 11) / (x^2 - 8x + 15)} - {3 / ( x-3)}

factoring each expression

x^2 - 8x + 15 = (x-3)(x-5)

we can write

2 / ( x-5 ) = ( x^2 - 2x - 11) / (x-3)(x-5) - 3 / ( x-3)

multiplying both sides by lcd which is (x-3)(x-5) we get

2 ( x-3) = ( x^2 - 2x - 11) - 3(x-5)

2x - 6 = ( x^2 - 2x - 11) - 3x + 15

2x - 6 = x^2 -5x + 4

bringing all terms on one side

x^2 -7x + 10 = 0

on solving the quadratic we get

(x-5)(x-2) = 0

x = 5 or x = 2

x cant be 5 since it will make the denominator 0 so we discard this value

hence the solution is x = 2