Question

the area of a rectangle is found by multiplying the base times the height. a rectangle with an area represented by 12x² + 6x - 8 has a height of 4x. what is the base of the rectangle? 3x + 3/2 - 2/x 3x² + 3/2 - 2/x 3x + 3x/2 - 2/x 3x + 3/2 - 1/2x

Explanation:

Step1: Recall area formula for rectangle

The area formula of a rectangle is $A = base\times height$. We know $A=12x^{2}+6x - 8$ and $height = 4x$. To find the base, we use the formula $base=\frac{A}{height}$, so $base=\frac{12x^{2}+6x - 8}{4x}$.

Step2: Divide each term in the numerator by the denominator

$\frac{12x^{2}}{4x}+\frac{6x}{4x}-\frac{8}{4x}$.

Step3: Simplify each fraction

For $\frac{12x^{2}}{4x}$, using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\frac{12}{4}x^{2 - 1}=3x$. For $\frac{6x}{4x}=\frac{6}{4}=\frac{3}{2}$. For $\frac{8}{4x}=\frac{2}{x}$.

Answer:

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