# Thread: Solving Complex Fractional Equations

1. ## Solving Complex Fractional Equations

$\displaystyle \frac{4m}{m-2}-\frac{13}{3m-6}=\frac{1}{3}$

I'm having problems finding a common denominator

2. (4 m)/(m-2)-13/(m-6) = 1/3

Multiply both sides by m-6:
(4 (m-6) m)/(m-2)-13 = (m-6)/3

Expand out terms on both sides:
(4 m^2)/(m-2)-(24 m)/(m-2)-13 = m/3-2

Write the left hand side as a single fraction:
(4 m^2-37 m+26)/(m-2) = m/3-2

Multiply both sides by m-2:
4 m^2-37 m+26 = 1/3 (m-2) m-2 (m-2)

Expand out terms on the right hand side:
4 m^2-37 m+26 = m^2/3-(8 m)/3+4

Subtract (m^2/3-(8 m)/3+4) from both sides:
(11 m^2)/3-(103 m)/3+22 = 0

Solve the quadratic equation by completing the square:

Divide both sides by 11/3:
m^2-(103 m)/11+6 = 0

Subtract 6 from both sides:
m^2-(103 m)/11 = -6

m^2-(103 m)/11+10609/484 = 7705/484

Factor the left hand side:
(m-103/22)^2 = 7705/484

Take the square root of both sides:
|m-103/22| = sqrt(7705)/22

Eliminate the absolute value:
m-103/22 = -sqrt(7705)/22 or m-103/22 = sqrt(7705)/22

m = 1/22 (103-sqrt(7705)) or m-103/22 = sqrt(7705)/22

m = 1/22 (103-sqrt(7705)) or m = 1/22 (103+sqrt(7705))

3. i dont understand it how u wrote it and the denominator was $\displaystyle \frac{13}{3m-6}$

4. oops. that would have made it much easier haha.

anyways m=1

do you need the steps?

5. yes I'm trying to understand.

6. factor out a 3 on the denominator of 3m-6

so you will have 3(m-2) so to get common denominators just multiple the other denominator and numerator of 4m/(m-2) by 3.

this will give you common denominators. can you solve for m from there?

7. Originally Posted by purplec16
$\displaystyle \frac{4m}{m-2}-\frac{13}{3m-6}=\frac{1}{3}$

I'm having problems finding a common denominator
note that $\displaystyle 3m-6 = 3(m-2)$

$\displaystyle \frac{3 \cdot 4m}{3(m-2)}-\frac{13}{3(m-2)}=\frac{1(m-2)}{3(m-2)}$

denominators are all the same ... the numerator forms the equation

$\displaystyle 12m - 13 = m-2$

solve for $\displaystyle m$ , remember that m cannot equal $\displaystyle 2$.

8. i got the 12m-13 but i dont get how u got the m-2

9. would be willing to help me with a few other questions at least by telling me if you got the same answers?

10. $\displaystyle \frac{4m}{m-2}-\frac{13}{3m-6}=\frac{1}{3}$

$\displaystyle \frac{3(4m)}{3(m-2)}-\frac{13}{3(m-2)}=\frac{1}{3}$

$\displaystyle \frac{12m-13}{3(m-2)}=\frac{1}{3}$

$\displaystyle \frac{12m-13}{m-2}=1$

$\displaystyle 12m-13 = m-2$

$\displaystyle 11m=11$
$\displaystyle m=1$

11. Originally Posted by purplec16
i got the 12m-13 but i dont get how u got the m-2
look at the numerator on right side of the equation ...

12. Originally Posted by purplec16
would be willing to help me with a few other questions at least by telling me if you got the same answers?

13. $\displaystyle \frac{3}{2b+4}-\frac{4}{b-2}=\frac{3}{2b^2-8}$