Question

Simplify. What are the restrictions on the variable? (2x/x-3)+(6/3-x)

Answer 1

Answer:

V = 2

x ≠ 3

Step-by-step explanation:

Simplifying

We are given the expression:

$\displaystyle V=\frac{2x}{x-3}+\frac{6}{3-x}$

To simplify, we make both denominators equal by multiplying the second term by -1:

$\displaystyle V=\frac{2x}{x-3}-\frac{6}{x-3}$

Now both denominators are equal, we simply add the numerators:

$\displaystyle V=\frac{2x-6}{x-3}$

Factoring the numerator:

$\displaystyle V=\frac{2(x-3)}{x-3}$

This expression can be simplified by x-3, but we must take into consideration the x-3 cannot be zero because it would cause an indetermination to appear.

The restriction is:

x - 3 ≠ 0

Or, equivalently:

x ≠ 3

Simplifying:

V = 2