Question

Solve: 1/(x^2-7x+10)=x/(x-5)+1/(x-2)

Answer 1

This one looks a little scary =S @jim_thompson5910

Answer 2

Don't worry, it's more afraid of you than you are of it lol

Answer 3

Haha, I hope so =)

Answer 4

1/(x^2-7x+10)=x/(x-5)+1/(x-2)


1/((x-5)(x-2))=x/(x-5)+1/(x-2)


(x-5)(x-2)[1/((x-5)(x-2))] =(x-5)(x-2)[x/(x-5)] + (x-5)(x-2)[1/(x-2)]


1 = x(x-2) + x-5


Do you see how I got this?

Answer 5

I think so =) Did you foil x^2-7x+10, then multiply that number by both sides?

Answer 6

I factored x^2-7x+10 to get (x-5)(x-2), then I multiplied everything by the LCD (x-5)(x-2) to clear out the fractions

Answer 7

I see! =)

Answer 8

So now, we do what next?

Answer 9

simplify to x^2-x-6=0

Answer 10

good, you got it, then what?

Answer 11

Plug into quadratic formula

Answer 12

bingo

Answer 13

I got -2 and 3

Answer 14

you nailed it once again

Answer 15

Yes! Thank you so much!! =)

Answer 16

as a general rule of thumb, it's best to always check your answers, but they both work (as I just checked them)