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Exercise

$\frac{9+\frac{1}{x}}{4-\frac{1}{x}}$

Step-by-step Solution

1

Combine $4+\frac{-1}{x}$ in a single fraction

$\frac{9+\frac{1}{x}}{\frac{-1+4x}{x}}$
2

Combine $9+\frac{1}{x}$ in a single fraction

$\frac{\frac{1+9x}{x}}{\frac{-1+4x}{x}}$
3

We can simplify the quotient of fractions $\frac{\frac{1+9x}{x}}{\frac{-1+4x}{x}}$ by inverting the second fraction and multiply both fractions

$\frac{\left(1+9x\right)x}{x\left(-1+4x\right)}$
4

Simplify the fraction $\frac{\left(1+9x\right)x}{x\left(-1+4x\right)}$ by $x$

$\frac{1+9x}{-1+4x}$

Final answer to the exercise

$\frac{1+9x}{-1+4x}$

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Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

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