Solve for b 3/x+5/(x^2)=(ax+b)/(x^2)

$\frac{3}{x} + \frac{5}{x^{2}} = \frac{a x + b}{x^{2}}$

Rewrite the equation as $\frac{a x + b}{x^{2}} = \frac{3}{x} + \frac{5}{x^{2}}$ .

$\frac{a x + b}{x^{2}} = \frac{3}{x} + \frac{5}{x^{2}}$

Multiply both sides by $x^{2}$ .

$\frac{a x + b}{x^{2}} x^{2} = (\frac{3}{x} + \frac{5}{x^{2}}) x^{2}$

Simplify.

Simplify the left side.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{a x + b}{x^{2}} x^{2} = (\frac{3}{x} + \frac{5}{x^{2}}) x^{2}$

Rewrite the expression.

$a x + b = (\frac{3}{x} + \frac{5}{x^{2}}) x^{2}$

Simplify the right side.

Simplify $(\frac{3}{x} + \frac{5}{x^{2}}) x^{2}$ .

Apply the distributive property.

$a x + b = \frac{3}{x} x^{2} + \frac{5}{x^{2}} x^{2}$

Cancel the common factor of $x$ .

Factor $x$ out of $x^{2}$ .

$a x + b = \frac{3}{x} (x \cdot x) + \frac{5}{x^{2}} x^{2}$

Cancel the common factor.

$a x + b = \frac{3}{x} (x \cdot x) + \frac{5}{x^{2}} x^{2}$

Rewrite the expression.

$a x + b = 3 x + \frac{5}{x^{2}} x^{2}$

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$a x + b = 3 x + \frac{5}{x^{2}} x^{2}$

Rewrite the expression.

$a x + b = 3 x + 5$

Subtract $a x$ from both sides of the equation.

$b = 3 x + 5 - a x$