Question

Solve for x :
8/x = 1 + 2/(x-2)

Please show step by step

Answer 1

do you know how to find the LCD?

Answer 2

Turn the problem into a proportion, then cross multiply. You'll get a quadratic that you can solve. Make sure to check your solutions against the domain at the end.

Answer 3

\[\frac{8}{x} = 1 + \frac{2}{(x-2)}=\frac{x}{x-2}\]Cross multiply and solve the quadratic equation.

Answer 4

how did you get x/x-2?

Answer 5

Common denominator of the RHS is x-2, so the one is (x-2)/(x-2). Add the numerators, and the twos cancel one another.

Answer 6

doesnt that give you 8x-10/x = 3?

Answer 7

Huh?

Answer 8

From my previous work, cross multiply to get\[8x-16=x^2 \implies x^2-8x+16=0 \implies (x-4)^2=0 \implies x=4\]

Answer 9

The solution x=4 solves the original problem.

Answer 10

i dont understand how you cross multiply and get x/x-2

Answer 11

i thought you needed to find a lcm

Answer 12

My chosen method for this problem is to make a proportion. That is a rational expression equal to another rational expression. From there, you can cross multiply.

If you multiply both sides of the original problem by the common denominator of the whole problem (in this case it is x^2-2x), you will get the same quadratic equation after some manipulation.

Answer 13

Alternate method....\[\frac{8}{x} = 1 + \frac{2}{(x-2)} \implies x(x-2)\frac{8}{x} =(1 + \frac{2}{(x-2)})x(x-2)\]\[\implies 8x-16=x^2-2x+2x \implies x^2-8x+16=0\]Exactly as before.

Answer 14

thanks so much i understood!

Answer 15

No sweat. Keep in mind that there are usually a few ways to do problems. Keep your mind open to various methods, and you might learn some ways that make problems easier.