Simplify:
2x+5/4x^2+2x-5/10x Please Show All Work!
To simplify the expression (2x + 5) / (4x^2 + 2x - 5) / (10x), we need to follow these steps:
1. Factorize the denominators:
4x^2 + 2x - 5 can be factored as (2x - 1)(2x + 5)
10x can be factored as 10 * x
2. Rewrite the expression using the factored form of the denominators:
[(2x + 5) / (2x - 1)(2x + 5)] / (10x)
3. Cancel out any common factors between the numerator and the denominator.
In this case, both the numerator and the denominator have a factor of (2x + 5), so we can cancel them out.
[(2x + 5) / (2x - 1)(2x + 5)] / (10x) = 1 / (2x - 1) / (10x)
4. Simplify the expression further:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Thus, 1 / (2x - 1) / (10x) = 1 * (10x) / (2x - 1)
Therefore, the simplified expression is (10x) / (2x - 1).