Question

How does one solve this rational expression: 6z/z-2=8? I have absolutely no idea how to solve expressions like this, so please go into detail.

Answer 1

\[\frac{ 6z }{z-2 }=8\]

Answer 2

Firstly multiply both sides of the equation by (z - 2). This will remove the fraction on the left hand side.

Answer 3

Now I have \[\frac{ 6z ^{2} }{z-2 ? }=\frac{ 8z-16 }{1 }\]

Answer 4

Correct?

Answer 5

Oh wait, I don't need to multiply the left because it already has z-2!

Answer 6

Or not. What am I thinking? Sorry.

Answer 7

\[\frac{6z}{z-2}\times \frac{z-2}{1}=6z=8(z-2)\]
\[6z=8(z-2)\]

Answer 8

How did you get rid of the 8 in the second step?

Answer 9

The first step shows two things. First the result of multiplying the left hand side of the original equation by (z - 2) and getting the result 6z. Next the result (6z) is put equal to the right hand side of the original equation which must also be multiplied by (z-2), getting 8(z - 2).
Do you follow?

Answer 10

Starting again. Multiply both sides of the original equation by (z - 2):
\[\frac{6z}{z-2}\times \frac{z-2}{1}=8\times \frac{z-2}{1}\]
On the left hand side the (z - 2) in the numerator and the denominator cancel each other and we get:
\[6z=8(z-2)\]

Answer 11

Yes, I follow that. In fact, when I worked out this equation an hour ago I got the same answer. Upon checking my answers in the textbook, I found that z is equal to 8. How does one find that?

Answer 12

You need to solve 6z = 8(z - 2) for z:
First multiply out the right hand side to remove the brackets. Can you do that?

Answer 13

That should be 6z= 8z-16. I guess that the 16 has to be transposed but I'm not sure how to go on from there. Thanks for staying here for so long, I really appreciate it.

Answer 14

Goodness, I'm so lost. This is pathetic.

Answer 15

Yes. Now add 16 to both sides giving:
6z + 16 = 8z - 16 + 16 = 8z
So now we have:
6z + 16 = 8z
Now subtract 6z from both sides. What do you get?

Answer 16

16=2z 16/2=8, so 8= z. I can't believe how long it takes for me to grasp these things. Thanks again for taking the time to help me out. I'll still have to re-read it but this cleared up a lot.

Answer 17

Good work!! Please keep practising and you will continue to improve :)