Question

What is the solution to the rational equation x over x squared minus 9 minus 1 over x minus 3 equals 1 over 4x minus 12 ?

Answer 1

the answer is b which is x=-15

Explanation:

Answer 2

`The\ domain\ (D):\\x^2-9\\eq0\ \wedge\ x-3\\eq0\ \wedge\ 4x-12\\eq0\\x^2\\eq9\ \wedge\ x\\eq3\ \wedge\ 4x\\eq12\\x\\eq-3\ \wedge\ x\\eq3\\\boxed{D:x\in\mathbb{R}-\{-3;\ 3\}}\\\\(x)/(x^2-9)-(1)/(x-3)=(1)/(4x-12)\\\\(x)/(x^2-3^2)-(1)/(x-3)=(1)/(4(x-3))\ \ \ \ |use\ a^2-b^2=(a-b)(a+b)\\\\(x)/((x-3)(x+3))-(1)/(x-3)=(1)/(4(x-3))\\\\(x\cdot4)/((x-3)(x+3)\cdot4)-(1(x+3)\cdot4)/((x-3)(x+3)\cdot4)=(1(x+3))/(4(x-3)(x+3))\\\\(4x-4(x+3))/(4(x-3)(x+3))=(x+3)/(4(x-3)(x+3))\iff4x-4x-12=x+3`


`x+3=-12\ \ \ \ |subtract\ 3\ from\ both\ sides\\\\\boxed{x=-15}\in D`