Question

Solve the Equation
1/(x-1)+6/(x+1)=8/(x^2-1)

Answer 1

Get common denominators first

Answer 2

how do i find the common denominator for this type of problem?

Answer 3

Factor out the denominators and see what they have on common and what they are missing

Answer 4

so (x-1}{x+1)(x^2-1) is the common denominator? right

Answer 5

Nope, you can factor that (x^2-1) you know

Answer 6

keep in mind that \(\bf x^2-1 \implies x^2-1^2\)

Answer 7

and that \(\bf (a-b)(a+b) = (a^2-b^2)\)

Answer 8

@jdoe0001 You wanna handle this?

Answer 9

ok

Answer 10

\(\bf \cfrac{1}{x-1}+\cfrac{6}{x+1}=\cfrac{8}{x^2-1} \implies
\cfrac{1}{x-1}+\cfrac{6}{x+1}=\cfrac{8}{x^2-1^2}\\
\implies \cfrac{1}{x-1}+\cfrac{6}{x+1}=\cfrac{8}{\square?}\)

Answer 11

so what do you think about \(\bf x^2-1^2\) ?

Answer 12

Got it, make sense, thanks. here is another one if you can help me with this.
16x-7/(8x+3)=2-3/x