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 = \square\\) \\(b = \square\\)

Explanation:

Step1: Get common denominator

To add the fractions on the left, rewrite $\frac{3}{x}$ with denominator $x^2$:
$\frac{3}{x} = \frac{3x}{x^2}$

Step2: Add the two fractions

Combine the fractions over the common denominator:
$\frac{3x}{x^2} + \frac{5}{x^2} = \frac{3x + 5}{x^2}$

Step3: Match to right-hand side

Compare $\frac{3x + 5}{x^2}$ with $\frac{ax + b}{x^2}$ to identify $a$ and $b$.

Answer:

$a = 3$
$b = 5$