Question

Solve: 7/(x-1)-5=6/(x^2-1)
Please help

Answer 1

is this
\[ \frac{7}{(x-1)} -5 = \frac{6}{(x^2-1)} \]?

Answer 2

yeah

Answer 3

can you factor (x^2 -1 ) ?

Answer 4

(x-1)(x+1)

Answer 5

\[ \frac{7}{(x-1)} -5 = \frac{6}{(x^2-1)} \]
can be written as
\[ \frac{7}{(x-1)} -5 = \frac{6}{(x-1)(x+1)} \]

I would multiply both sides of the equation (and *all* terms) by (x-1)(x+1)

can you do that ?

Answer 6

yeah
7(x+1)-5(x^2-1)=6
7x+7-5x^2+5=6
-5x^2+7x+2=6

Answer 7

then do i just factor that?

Answer 8

I would first bring the 6 over to the left side
-5x^2 + 7 x -4 =0

now (because I don't like leading minus signs), multiply both sides by -1 to get
5x^2 -7x +4 = 0

Answer 9

ok, so then do i use the quadratic formula?

Answer 10

looks like we have to

Answer 11

although check your arithmetic

7x+7-5x^2+5=6
this is ok, but the next line looks wrong: -5x^2+7x+2=6

Answer 12

oh, its +13, isn't it?

Answer 13

no, +12

Answer 14

and then 12 - 6 (bring the 6 over from the right side)

I am expecting that whatever we get should factor.

Answer 15

ok, so then after multiplying by -1 it's 5x^2-7x-6=0

Answer 16

yes

Answer 17

ok, so x=2 and x=-3/5

Answer 18

yes, looks good.

Answer 19

ok, thankyou :)

Answer 20

yw