what is the product?\n$\frac{2a - 7}{a}cdot\frac{3a^{2}}{2a^{2}-11a + 14}$\n$\frac{3}{a - 2}$\n$\frac{3a}{a…

what is the product?\n$\frac{2a - 7}{a}cdot\frac{3a^{2}}{2a^{2}-11a + 14}$\n$\frac{3}{a - 2}$\n$\frac{3a}{a - 2}$\n$\frac{3a}{a + 2}$\n$\frac{3}{a + 2}$

what is the product?\n$\frac{2a - 7}{a}cdot\frac{3a^{2}}{2a^{2}-11a + 14}$\n$\frac{3}{a - 2}$\n$\frac{3a}{a - 2}$\n$\frac{3a}{a + 2}$\n$\frac{3}{a + 2}$

Answer

Explanation:

Step1: Factor the quadratic expression

Factor (2a^{2}-11a + 14). We need two numbers that multiply to (2\times14 = 28) and add up to (-11). The numbers are (-4) and (-7). So (2a^{2}-11a + 14=2a^{2}-4a-7a + 14=2a(a - 2)-7(a - 2)=(2a - 7)(a - 2)).

Step2: Rewrite the product of fractions

The original product (\frac{2a - 7}{a}\cdot\frac{3a^{2}}{2a^{2}-11a + 14}) becomes (\frac{2a - 7}{a}\cdot\frac{3a^{2}}{(2a - 7)(a - 2)}).

Step3: Simplify the fraction

Cancel out the common factors ((2a - 7)) and (a). (\frac{2a - 7}{a}\cdot\frac{3a^{2}}{(2a - 7)(a - 2)}=\frac{3a}{a - 2}).

Answer:

(\frac{3a}{a - 2})