Question

What is the solution to the rational equation

Answer 1

+

Answer 2

=

Answer 3

@phi

Answer 4

you could practice using the equation editor

Answer 5

I would first factor the denominator of the very first fraction
can you do that ?

Answer 6

First factor all denominators. Then multiply both sides by the LCD. This will eliminate all denominators.

Answer 7

hhaha how do i use the equation editor?

Answer 8

yes i can!!

Answer 9

click on the equation button below the input area in the lower left. you can play with it : learn by doing...

meanwhile, can you factor the bottom of the first fraction ?

Answer 10

thanks and yes

Answer 11

what do you get ?

Answer 12

wait what am i looking for if it tells me what it equals

Answer 13

eventually, we will find x = something

Answer 14

you should get so far:
\[ \frac{5}{(x-2)(x-1) }+ \frac{1}{x-2} = \frac{1}{3(x-1) } \]

Answer 15

One good strategy is multiply both sides by (x-2). that means all terms on both sides of the =.
what do you get ?

Answer 16

huh??? what do i multiply that with?

Answer 17

do you see how we get
\[ \frac{5}{(x-2)(x-1) }+ \frac{1}{x-2} = \frac{1}{3(x-1) } \]?

Answer 18

We start with
\[ \frac{5}{x^2-3x+2 }+ \frac{1}{x-2} = \frac{1}{3x-3 } \]

factor the bottom of the first fraction. that means re-write as(x-2)(x-1)
factor out a 3 in the last fraction: 3(x-1)
we get our new equation