Find the Quotient ((2x-5)/4)÷((x+3)/4)

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

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

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

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

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

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

$\frac{x}{4}$

$\frac{3}{4}$

$\frac{2 x}{4}$

$\frac{- 5}{4}$

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

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

Multiply the new quotient term by the divisor.

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

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

The quotient is $2$ .

$2$