\frac{2x^2+13x+15}{4x^2-9}\ \div \frac{10x-15}{x^2+5x}

Answer 1

We can simplify the given expression by multiplying by the reciprocal of the second fraction:

\frac{2x^2 + 13x + 15}{4x^2 - 9} \times \frac{x^2 + 5x}{10x - 15}

First, factorize the numerator and denominator of the first fraction:

\frac{(2x + 3)(x + 5)}{(2x + 3)(2x - 3)} \times \frac{x(x + 5)}{5(2x - 3)}

Now, we can cancel out the common factors:

\frac{(x + 5)}{2x - 3} \times \frac{x}{5}

Finally, multiply the numerators and denominators:

\frac{x(x + 5)}{5(2x - 3)}

Therefore, the simplified expression is \frac{x(x + 5)}{5(2x - 3)}.