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
From your description, here is what you seem to have:
(x+2)/x + (x-2)/2x
Multiply by 2x
2x + 4 + x - 2 = 3x +2
I hope this helps. Thanks for asking.
To simplify the expression (x + 2) / (x^2 + x - 2) + (x - 2) / (2x), you need to combine the two fractions into one fraction by finding a common denominator.
First, let's factorize the denominators in both fractions:
1. x^2 + x - 2:
This expression can be factored as (x + 2)(x - 1).
2. 2x:
This expression is already in its simplest form.
Now we can rewrite the original expression with the factored denominators:
(x + 2) / [(x + 2)(x - 1)] + (x - 2) / (2x)
Next, let's find the common denominator, which is the product of both denominators:
Common denominator = (x + 2)(x - 1)(2x)
To make the first fraction have the common denominator, multiply the numerator and denominator by (2x):
[(x + 2) * (2x)] / [(x + 2)(x - 1)(2x)] + (x - 2) / (2x)
Now, the expression becomes:
[2x(x + 2)] / [(x + 2)(x - 1)(2x)] + (x - 2) / (2x)
Now, add the two fractions:
[2x(x + 2) + (x - 2)(x + 2)] / [(x + 2)(x - 1)(2x)]
Simplify the numerator:
[2x^2 + 4x + x^2 - 2x - 4] / [(x + 2)(x - 1)(2x)]
Combine like terms in the numerator:
[3x^2 + 2x - 4] / [(x + 2)(x - 1)(2x)]
Thus, the simplified expression is:
(3x^2 + 2x - 4) / [(x + 2)(x - 1)(2x)]