Question

Please help me with this problem thank you✨

Answer 1

x ≈ 8.37819064728

Explanation:

Maybe you want to solve for x.

`(x-4)/(x-3)=(2x^2-6)/(x^2+2x-3)-(x-1)/(x+1)=(2(x^2-3))/((x-1)(x+3))-(x-1)/(x+1)\\\\(x-4)/(x-3)=(2(x^2-3)(x+1))/((x-1)(x+3)(x+1))-((x-1)(x-1)(x+3))/((x+1)(x-1)(x+3))\\\\(x-4)/(x-3)=((2x^3+2x^2-6x-6)-(x^3+x^2-5x+3))/((x^2-1)(x+3))\\\\((x^2-1)(x+3)(x-4))/((x^2-1)(x+3)(x-3))=((x^3+x^2-x-9)(x-3))/((x^2-1)(x+3)(x-3))\\\\(x^4-x^3-13x^2+x+12)/((x^2-1)(x^2-9))=(x^4-2x^3-4x^2-6x+27)/((x^2-1)(x^2-9))\\\\(x^3-9x^2+7x-15)/((x^2-1)(x^2-9))=0`

A graphing calculator shows the numerator cubic to have one real irrational zero near x ≈ 8.37819064728.