Question

enter the values for a and b that complete the sum: \\(\frac{3}{x}+\frac{5}{x^2}=\frac{ax + b}{x^2}\\) \\(a = 3\\) \\(b = 5\\) enter the values for m, n, and p that complete the difference: \\(\frac{7}{x}-\frac{3}{2}=\frac{n - mx}{px}\\) \\(m = \square\\) \\(n = \square\\) \\(p = \square\\)

Explanation:

Step1: Find common denominator

To subtract $\frac{7}{x}$ and $\frac{3}{2}$, use common denominator $2x$.

Step2: Rewrite fractions

$$\frac{7}{x} - \frac{3}{2} = \frac{7 \times 2}{2x} - \frac{3 \times x}{2x} = \frac{14 - 3x}{2x}$$

Step3: Match to given form

Compare $\frac{14 - 3x}{2x}$ with $\frac{n - mx}{px}$.

Answer:

$m = 3$
$n = 14$
$p = 2$