Answer
$\dfrac{3x - 8}{4x^2}$
Restriction: $x \ne 0$
Work Step by Step
Before performing the subtraction, find the least common denominator (LCD) of the two fractions. The LCD is $4x^2$.
Convert the original fractions to equivalent fractions using the LCD:
$\dfrac{3x}{4x^2} - \dfrac{8}{4x^2}$
Subtract the fractions:
$=\dfrac{3x - 8}{4x^2}$
Restrictions on $x$ occur when the value of $x$ makes the fraction undefined, which happens that the denominator becomes $0$.
Set the denominators equal to $0$ to find restrictions:
First denominator:
$4x = 0$
Divide both sides by $4$:
$x = 0$
Second denominator:
$x^2 = 0$
Take the square root:
$x = 0$
Thus, the only restriction is: $x \ne 0$
