Simplify:
2x+5/4x^2+2x-5/10x
Please Show All Work!
To simplify the expression (2x + 5) / (4x^2 + 2x - 5) / (10x), we first need to find a common denominator for both fractions in the expression.
The common denominator is found by multiplying the denominators of the two fractions together. In this case, the denominators are (4x^2 + 2x - 5) and (10x). So the common denominator is (4x^2 + 2x - 5) * (10x).
Next, we need to multiply the numerator of the first fraction (2x + 5) by the denominator of the second fraction (10x), and the numerator of the second fraction (1) by the denominator of the first fraction (4x^2 + 2x - 5).
The simplified expression becomes:
[(2x + 5) * (10x)] / [(4x^2 + 2x - 5) * (10x)]
Expanding the numerator and the denominator:
[20x^2 + 50x] / [40x^3 + 20x^2 - 50x^2 + 20x - 50x]
Combining like terms:
[20x^2 + 50x] / [40x^3 - 30x^2 + 20x]
Now, we can simplify the expression by factoring out a common factor of 10x from the numerator and denominator:
(10x * (2x + 5)) / (10x * (4x^2 - 3x + 2))
Cancelling out the common factors:
(2x + 5) / (4x^2 - 3x + 2)
This is the simplified form of the expression.