Simplify the following algebraic expressions: A) −18x/2 B) −3x/−9x C) 3ab/ab D) (5x+2x-x)/2x E) (2x2-8x)/2x…

Question

Simplify the following algebraic expressions: A) −18x/2 B) −3x/−9x C) 3ab/ab D) (5x+2x-x)/2x E) (2x2-8x)/2x F) (5x2+x2)/−3

ScanSolve AI Tutor · Accepted Answer

Here are the simplified expressions:

A)

Divide the numerical coefficients.
$\frac{-18x}{2} = \left(\frac{-18}{2}\right)x = -9x$
The simplified expression is $\boxed{-9x}$ .

B)
Simplify the fraction by canceling out common terms.
$\frac{-3x}{-9x} = \frac{-3}{-9} \cdot \frac{x}{x} = \frac{1}{3} \cdot 1 = \frac{1}{3}$
The simplified expression is $\boxed{\frac{1}{3}}$ .

C)
Cancel out the common term $ab$ from the numerator and denominator.
$\frac{3ab}{ab} = 3 \cdot \frac{ab}{ab} = 3 \cdot 1 = 3$
The simplified expression is $\boxed{3}$ .

D)
Simplify the numerator by combining like terms.
$5x+2x-x = (5+2-1)x = 6x$
Substitute the simplified numerator back into the expression and simplify.
$\frac{6x}{2x} = \frac{6}{2} \cdot \frac{x}{x} = 3 \cdot 1 = 3$
The simplified expression is $\boxed{3}$ .

E)
Divide each term in the numerator by the denominator.
$\frac{2x^2-8x}{2x} = \frac{2x^2}{2x} - \frac{8x}{2x}$
Simplify each term.
$\frac{2x^2}{2x} = x$ $\frac{8x}{2x} = 4$
Combine the simplified terms.
$x - 4$
The simplified expression is $\boxed{x-4}$ .

F)
Simplify the numerator by combining like terms.
$5x^2+x^2 = (5+1)x^2 = 6x^2$
Substitute the simplified numerator back into the expression and simplify.
$\frac{6x^2}{-3} = \left(\frac{6}{-3}\right)x^2 = -2x^2$
The simplified expression is $\boxed{-2x^2}$ .

Simplify the following algebraic expressions: A) -18x/2 B) -3x/-9x C) 3ab/ab D) (5x+2x-x)/2x E) (2x2-8x)/2x F) (5x2+x2)/-3