Question

Solving rational equations. Solve each equation and find LCD 6/x-1+2x/x-2=2

Answer 1

First, you've gotta multiply the two denominators together to be able to add the numerators.
So (x-1)(x-2), the fraction will end up looking like this:
\[\frac{ 6+2x }{ x ^{2}-3x+2 }=2\]
Your LCD (least common denominator) is x^2-3x+2
Do you know what to do next to solve? :)

Answer 2

No

Answer 3

Okiedoke, you wanna get x by itself, so the first thing you'd do is multiply both sides of the equation by the denominator, because it will cancel out on the left and leave this:
6+2x=2(x^2-3x+2)
Distribute..
6+2x=2x^2-6x+4
Combine like terms..
0=2x^2-8x-2

At this point you use the quadratic formula to solve
\[\frac{ -b + or - \sqrt{b ^{2}-4ac} }{ 2a }\]
Your a=2, b=-8, c=-2
So plug those in and it'll look like:
\[\frac{ 8 + or - \sqrt{64+16} }{ 4 }\]
Simplify and it'll be:
\[\frac{ 8 + or - \sqrt{80} }{ 4 }\]
The sqrt80 can be divided to be sqrt16 times sqrt5, so it'll simplify to 4sqrt5 and look like:
\[\frac{ 8 + or - 4\sqrt{5} }{ 4 }\]
Now you can divide everything up top by the 4 below and you're left with:
\[2+ or - \sqrt{5}\]

So the solutions are 2+sqrt5 and 2-sqrt5

Hope that helps!!