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 
$$a(2x -a) = b(4x-b)?$$
 A: The process done is called Cross-multiplication.
This technique is generally used to work faster, we can solve such problems in 1 step rather than 2.
Let's say we have the following equation:
$$\frac{a}{b}=\frac{c}{d}$$
We can do it this way, without cross-multiplication:
Multiply both sides by $b$:
$$a=\frac{c}{d} b$$
Multiply both sides by $d$:
$$ad=bc$$
Now, let's use cross-multiplication:
$$\frac{\color{red}a}{\color{blue}b}=\frac{\color{blue}c}{\color{red}d}$$
We multiply the red and blue terms only.
$$\color{red}{ad}=\color{blue}{bc}$$
Now apply the same technique to the equation in your picture, and you should get the answer you were looking for.
A: 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.
A: Just cross multiply terms.
(2x - a) * a = (4x - b) * b
Which can be written as -
a(2x - a) = b(4x - b)
A: Multiply by $ab$ on both sides.
A: As other have called it: cross-multiplying (or taking cross-products). 
The thing I wanted to add to this answer is that, to my significant embarrassment, I just realized the other day that this is in fact the formal definition of fraction equality: $\frac{a}{b} = \frac{c}{d} \Leftrightarrow ad = bc$. (Which makes sense: operations on fractions need to be defined in terms of some pre-existing entity, namely integers.)
So another way of putting it is: we are directly applying the definition of equality for fractions.
https://en.wikipedia.org/wiki/Rational_number#Formal_construction
