Answer:
[tex]x=\frac{(a^2+ab)}{a-b}[/tex]
Step-by-step explanation:
So we want to make x the subject of the formula:
[tex]a(x-b)=a^2+bx[/tex]
First, distribute the left side:
[tex]a(x)-a(b)=a^2+bx\\ax-ab=a^2+bx[/tex]
Combine all the terms with x with it on one side. To do this, first subtract bx from both sides. The right side cancels:
[tex](ax-ab)-bx=(a^2+bx)-bx\\ax-ab-bx=a^2[/tex]
Remove the -ab from the left. Add ab to both sides. The left side cancels:
[tex](ax-ab-bx)+ab=a^2+ab\\ax-bx=a^2+ab[/tex]
Now, distribute out the x from the left side:
[tex]ax-bx=a^2+ab\\x(a-b)=a^2+ab[/tex]
Divide both sides by (a-b). The left side cancels:
[tex]\frac{(x(a-b))}{a-b}=\frac{(a^2+ab)}{a-b} \\x=\frac{(a^2+ab)}{a-b}[/tex]
Therefore:
[tex]x=\frac{(a^2+ab)}{a-b}[/tex]
