# Math Help - Solving Algebraically.

1. ## Solving Algebraically.

Solving Algebraically.
1/x+1/3x=x/12
I got to 36x+12x=3x^3, tell me if I am wrong! Many thanks!

2. Originally Posted by BabyMilo
Solving Algebraically. I got to 36x+12x=3x^3, tell me if I am wrong! Many thanks!
Yes, you are wrong.

You have $\frac{1}{x}+ \frac{3}{x}= \frac{1}{12}$
The "common denominator" is 12x so you can get rid of the fractions by multiplying the entire equation by 12x. Simplify the fractions in $\frac{12x}{x}+ \frac{3(12x)}{x}= \frac{12x}{12}$

3. Originally Posted by HallsofIvy
Yes, you are wrong.

You have $\frac{1}{x}+ \frac{3}{x}= \frac{1}{12}$
The &quot;common denominator&quot; is 12x so you can get rid of the fractions by multiplying the entire equation by 12x. Simplify the fractions in $\frac{12x}{x}+ \frac{3(12x)}{x}= \frac{12x}{12}$

4. $\frac{1}{x}+\frac{1}{3x}=\frac{x}{12}$ $\Rightarrow$
$3(\frac{1}{x})+\frac{1}{3x}=\frac{x}{12}$ $\Rightarrow$
$\frac{3}{3x}+\frac{1}{3x}=\frac{x}{12}$ $\Rightarrow$
$\frac{3+1}{3x}=\frac{x}{12}$ $\Rightarrow$
$\frac{4}{3x}=\frac{x}{12}$ $\Rightarrow$

4(12)=x(3x) $\Rightarrow$ 48=3 $x^2$ $\Rightarrow$ 3 $x^2$-48=0 $\Rightarrow$

3( $x^2$-16)=0 $\Rightarrow$ ( $x^2$-16)=0 $\Rightarrow$ $x^2$=16 $\Rightarrow$

x=4 or x=-4

5. Originally Posted by SENTINEL4
$\frac{1}{x}+\frac{1}{3x}=\frac{x}{12}$ $\Rightarrow$
$3(\frac{1}{x})+\frac{1}{3x}=\frac{x}{12}$ $\Rightarrow$
$\frac{3}{3x}+\frac{1}{3x}=\frac{x}{12}$ $\Rightarrow$
$\frac{3+1}{3x}=\frac{x}{12}$ $\Rightarrow$
$\frac{4}{3x}=\frac{x}{12}$ $\Rightarrow$

4(12)=x(3x) $\Rightarrow$ 48=3 $x^2$ $\Rightarrow$ 3 $x^2$-48=0 $\Rightarrow$

3( $x^2$-16)=0 $\Rightarrow$ ( $x^2$-16)=0 $\Rightarrow$ $x^2$=16 $\Rightarrow$

x=4 or x=-4
Many Thanks! I know it's right as I have checked but where did you get the 3 from on the second line?

6. $\frac{1}{x}+\frac{1}{3x}$ we have these two fractions which are disimilar. We want similar fractions to add them. Similar fractions are those which have same denominators (bottom number).
Here the two denominators are x and 3x, so we multiply the first fraction with 3 (both numerator and denominator) and we have $\frac{3}{3x}$.
Now that are similar we add their numerators.

I hope i make you understand, english isn't my mother language