which expression is equivalent to $\frac{2a + 1}{10a - 5}div\frac{10a}{4a^{2}-1}$?\n$\frac{2a}{(2a…

which expression is equivalent to $\frac{2a + 1}{10a - 5}div\frac{10a}{4a^{2}-1}$?\n$\frac{2a}{(2a - 1)^{2}}$\n$\frac{50a}{(2a + 1)^{2}}$\n$\frac{(2a - 1)^{2}}{2a}$\n$\frac{(2a + 1)^{2}}{50a}$

which expression is equivalent to $\frac{2a + 1}{10a - 5}div\frac{10a}{4a^{2}-1}$?\n$\frac{2a}{(2a - 1)^{2}}$\n$\frac{50a}{(2a + 1)^{2}}$\n$\frac{(2a - 1)^{2}}{2a}$\n$\frac{(2a + 1)^{2}}{50a}$

Answer

Explanation:

Step1: Factor the expressions

Factor the denominators and numerators. $10a - 5=5(2a - 1)$, $4a^{2}-1=(2a + 1)(2a - 1)$. The division $\frac{2a + 1}{10a - 5}\div\frac{10a}{4a^{2}-1}$ can be rewritten as $\frac{2a + 1}{5(2a - 1)}\times\frac{(2a + 1)(2a - 1)}{10a}$ (since dividing by a fraction is the same as multiplying by its reciprocal).

Step2: Simplify the product

Multiply the numerators and denominators: $\frac{(2a + 1)\times(2a + 1)(2a - 1)}{5(2a - 1)\times10a}$. Cancel out the common factor $(2a - 1)$ in the numerator and denominator. We get $\frac{(2a + 1)^{2}}{50a}$.

Answer:

$\frac{(2a + 1)^{2}}{50a}$