Answer:
Step-by-step explanation:
First, Let's take a on both sides:
[tex]\frac{1}{x}+a-a=b-a[/tex]
[tex]\frac{1}{x}=b-a[/tex]
Remember that 1/x is called the reciprocal. For example the reciprocal of 2 is 1/2 and the reciprocal of 5 is 1/5. If we read the equation is telling us: "Reciprocal of x is b - a". Therefore, [tex]\frac{1}{b-a}=x[/tex].
Another way to solve it is to multiply x on both sides. Then,
[tex]\frac{x}{x}=(b-a)*x[/tex]
[tex]1=(b-a)*x[/tex]
Then divide by (b-a). Remmebre to treat b-a as a factor:
[tex]\frac{1}{(b-a)}=\frac{(b-a)*x}{(b-a)}[/tex]
Cancelling (b-a) on the right hand side:
[tex]\frac{1}{(b-a)}=x[/tex]
