## anonymous 5 years ago 8x/(x-8)(x-10)=9x+2

1. anonymous

Is this $$\frac{8x}{(x-8)(x-10)} = 9x+2$$?

2. anonymous

yes

3. anonymous

The first thing you want to do is get rid of the denominator by multiplying it to the other side.

4. anonymous

so the entire (x-8)(x-10)

5. anonymous

Be careful, you can multiply the denominator to the other side provided the x is not 8 or x is not 10, otherwise we cannot just simply multiply like that

6. anonymous

you can't multiply...

7. anonymous

what do i do then?

8. anonymous

8x/(x-8)(x-10)=9x+2 [8x/(x-8)(x-10)] -(9x+2) = 0 [8x -(9x+2)(x-8)(x-10)] / [(x-8)(x-10)] = 0 for the fraction on the left to be zero, the numerator must be zero. So 8x -(9x+2)(x-8)(x-10) = 0

9. anonymous

That is the explanation, but as you can see, it has the same effect as multiply the denominator to the right side and then bring the right side to the left..

10. anonymous

now i jsut solve>?

11. anonymous

Yep. The key to problems that have variables in the denominator is checking your answers when you solve. If you get that $$x=8$$ or $$x=10$$ once you solve, you have to say that these aren't valid answers, because they would make the denominator equal zero.