Answer:
[tex]x=\frac{abc}{b+a}[/tex]
Step-by-step explanation:
So we have:
[tex]\frac{x}{a}+\frac{x}{b}=c[/tex]
And we want to solve for x.
To do so, let's remove the fractions. We can multiply both sides by the LCM of a and b, which is ab. So:
[tex](ab)\frac{x}{a}+\frac{x}{b}=c(ab)[/tex]
On the left, distribute. On the right, multiply:
[tex]\frac{x(ab)}{a}+\frac{x(ab)}{b}=abc[/tex]
Simplify:
[tex]xb+xa=abc[/tex]
Now, factor out an x on the left:
[tex]x(b+a)=abc[/tex]
Divide both sides by (b+a):
[tex]x=\frac{abc}{b+a}[/tex]
And we're done!
