simplify:
x+2
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x to the second power + x-2
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2x
X+2 divided by x to the second power plus x-2 divided by 2x
To simplify the expression (x+2)/(x^2 + x - 2)/(2x), we can follow these steps:
Step 1: Factorize the denominators:
The denominator x^2 + x - 2 can be factored as (x - 1)(x + 2).
The denominator 2x can't be factorized further.
Step 2: Rewrite the expression as a fraction multiplication:
We can rewrite the expression as (x+2)/(x - 1)(x + 2) * 2x.
Step 3: Simplify by canceling out common factors:
Notice that (x + 2) appears in both the numerator and denominator. We can cancel them out, leaving us with:
(x + 2)/(x - 1) * 2x
Step 4: Simplify the expression further, if needed:
If we distribute 2x to (x + 2)/(x - 1), we get:
2x * (x + 2) / (x - 1)
The final simplified expression is:
2x(x + 2) / (x - 1)
To simplify the expression (x+2)/(x^2 + x-2)/(2x), we can begin by dividing the first fraction by the second fraction, which is equivalent to multiplying the first fraction by the reciprocal of the second fraction.
The reciprocal of (x^2 + x-2)/(2x) is (2x)/(x^2 + x-2).
Therefore, the expression simplifies to:
(x+2) * (2x)/(x^2 + x-2)
Now, we can simplify further by multiplying the numerators and denominators together:
2x(x+2) / (x^2 + x-2)
The simplified expression is 2x(x+2) / (x^2 + x-2).