Math Snap

STEP 1

Assumptions1. The expression to be simplified is $\frac{4}{x^{}-4}+\frac{3 \cdot x}{x-}+1$.
. We are allowed to use the algebraic rules of simplification.

STEP 2

We can simplify the expression by first factoring the denominator of the first term.
$$x^{2}-4 = (x-2)(x+2)$$So, the expression becomes$$\frac{4}{(x-2)(x+2)}+\frac{ \cdot x}{x-2}+1$$

STEP 3

Next, we can find a common denominator for the fractions. In this case, the common denominator is $(x-2)(x+2)$.So, we rewrite each term with the common denominator$$\frac{}{(x-2)(x+2)}+\frac{3 \cdot x \cdot (x+2)}{(x-2)(x+2)}+\frac{(x-2)(x+2)}{(x-2)(x+2)}$$

STEP 4

Now, we simplify the numerators$$\frac{4 +3x^{2} +6x + x^{2} -4}{(x-2)(x+2)}$$

STEP 5

Combine like terms in the numerator$$\frac{4x^{2} +x}{(x-2)(x+2)}$$

Factor out the common factor in the numerator$$\frac{2x(2x +3)}{(x-2)(x+2)}$$This is the simplified form of the original expression.