## Kamille 3 years ago I need to find x: (a+x)/(b-x)=(4a)/(3b) Anyone has any ideas?

1. Kamille

Also, I know that $b \neq 0$ and $b \neq x$

2. Kamille

$(\frac{ a+x }{ b-x } )=\frac{ 4a }{ 3b }$

3. kropot72

First multiply both sides by (b - x) to eliminate the fraction of the left hand side. Then multiply both sides of the result by 3b to eliminate the fraction on the right hand side. Can you do that?

4. Kamille

Well, I get this. If you have time, can you look? (a+x)/(b-x)=(4a/3b)|*(b-x) a+x=4a/3b(b-x)|*3b 3ba+3bx=4a/b-x

5. Kamille

If you wont understand what I get, i can use "equation" to show.

6. kropot72

Multiplying both sides by (b - x) gives: $\frac{a+x}{b-x}\times (b-x)=\frac{4a(b-x)}{3b}$ $a+x=\frac{4a(b-x)}{3b}$ Now multiplying both sides by 3b gives: $3b(a+x)=4a(b-x)$ Do you follow so far?

7. Kamille

Well, I understand this. What to do next?

8. kropot72

Next multiply out to remove the brackets, then rearrange to get the two terms in x on the left hand side.

9. kropot72

Finally you factorise out x and perform a division to get: $x=\frac{?}{?}$

10. Kamille

Oh,thank you very much. 3ba+3bx=4ab-4ax 3bx=4ab-3ab-4ax 3bx+4ax=ab x(3b+4a)=ab x=ab/3b+4a correct?

11. kropot72

12. Kamille

Thank you very much:))

13. kropot72

You're welcome :)