how do you solve x^2-4/x^2-4+4 x 2x-4/x+2
it will be easier if you provide some parentheses so we can interpret the problem.
Noticing how everything matches up nicely I am sure you meant to type
( (x^2-4)/(x^2 - 4x + 4) )( (2x-4)/(x+2) )
= [(x+2)(x-2)/(x-2)^2][2(x-2)/(x+2)]
= 2 , where x ≠ ±2
To solve the given expression, we'll simplify it step by step using basic algebraic operations. Let's break it down:
Step 1: Rewrite the expression with proper grouping symbols to denote the numerator and denominator more clearly.
(x^2 - 4) / (x^2 - 4) + (4x (2x - 4)) / (x + 2)
Step 2: Factorize the numerator and denominator where possible.
(x^2 - 4) can be factored to (x - 2) (x + 2).
Step 3: Simplify the expression by canceling out any common factors.
[(x - 2) (x + 2)] / [(x - 2) (x + 2)] + [(4x) (2x - 4) / (x + 2)]
Step 4: Cancel out the common factors.
We can cancel out (x - 2) and (x + 2) from the numerator and denominator.
Step 5: Rewrite the simplified expression without the canceled factors.
1 + 4x (2x - 4) / (x + 2)
Step 6: Simplify further if possible.
The expression 4x (2x - 4) can be rewritten as 8x^2 - 16x.
Step 7: Replace the simplified expression back into the original equation.
1 + (8x^2 - 16x) / (x + 2)
So, the simplified form of the given expression is 1 + (8x^2 - 16x) / (x + 2).