Linear equation with different variable on the denominator? I have this given problem. That asking me to solve for $x$. Although this example has answered. I've had troubles on a certain part.
Here's the equation with answer

\begin{align*}
\frac{2x-a}b &= \frac{4x-b}a\\
a(2x-a) &= b(4x-b) \\
2ax-a^2 &= 4bx - b^2 \\
2ax-4bx &= a^2 - b^2 \\
x(2a-4b) &= a^2 - b^2 \\
x&=\frac{a^2-b^2}{2a-4b}
\end{align*}

How did we arrive to 
$$a(2x -a) = b(4x-b)?$$

Maybe we need to write again the equation:
$$\frac{2x-a}{b}=\frac{4x-b}{a}.$$
Using the Multiplication Property of Equality, we get
$$ab\cdot\left(\frac{2x-a}{b}\right)=ab\cdot\left(\frac{4x-b}{a} \right).$$
Simplifying, we get
$$\frac{a\cdot b\cdot (2x-a)}{b}=\frac{a\cdot b\cdot (4x-b)}{a}.$$
Apply Cancellation Law in Multiplication (meaning we can cancel $b$ at the left hand side and same to $a$ at the right hand side), we get
$$a\cdot(2x-a)=b\cdot(4x-b).$$
Hope this help.
