Algebra Examples

$\frac{2 x - 5}{4} \div \frac{x + 3}{4}$

Step 1

Split the fraction $\frac{2 x - 5}{4}$ into two fractions.

$\frac{\frac{2 x}{4} + \frac{- 5}{4}}{\frac{x + 3}{4}}$

Step 2

Split the fraction $\frac{x + 3}{4}$ into two fractions.

$\frac{\frac{2 x}{4} + \frac{- 5}{4}}{\frac{x}{4} + \frac{3}{4}}$

Step 3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$\frac{x}{4}$

$\frac{3}{4}$

$\frac{2 x}{4}$

$\frac{- 5}{4}$

Step 4

Divide the highest order term in the dividend $\frac{2 x}{4}$ by the highest order term in divisor $\frac{x}{4}$ .

					$2$
	$\frac{x}{4}$	+	$\frac{3}{4}$		$\frac{2 x}{4}$	+	$\frac{- 5}{4}$

Step 5

Multiply the new quotient term by the divisor.

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $\frac{x}{2} + \frac{3}{2}$

Step 7

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 8

The final answer is the quotient plus the remainder over the divisor.

$2 - \frac{11}{4 (\frac{x}{4} + \frac{3}{4})}$