How do you simplify #(4x+8) /( 3x)* (9x^2) / (x+2)#?

Question

Genesis Allen · Accepted Answer

#E = 12x#

Your starting expression is

#E = (4x+8)/(3x) * (9x^2)/(x+2)#

You can simplify this expression by factoring the numerator of the first fraction and cancelling like terms that can be found on the numerator and denominator of the resulting fraction.

The numerator of the first fraction can be rewritten as

#4x+8 = 3 * (x+2)#

Likewise, you can write the numerator of the second fraction as

#9x^2 = (3x)^2 = 3x * 3x#

This means that you have

#E = (4 * color(red)(cancel(color(black)((x+2)))))/(color(blue)(cancel(color(black)(3x)))) * (color(blue)(cancel(color(black)(3x))) * 3x)/color(red)(cancel(color(black)((x+2)))) = 4 * 3x = color(green)(12x)#

Hazel Anglin · Answer

undefined To simplify the expression (4x+8) / (3x) * (9x^2) / (x+2), we can follow these steps:

1. Simplify each fraction separately:
   - (4x+8) / (3x) simplifies to (4(x+2)) / (3x)
   - (9x^2) / (x+2) remains as it is.

2. Multiply the simplified fractions together:
   - (4(x+2)) / (3x) * (9x^2) / (x+2)

3. Cancel out any common factors between the numerators and denominators:
   - The (x+2) terms cancel out.

4. Multiply the remaining terms together:
   - (4 * 9x^2) / (3x)

5. Simplify the expression further:
   - (36x^2) / (3x)

6. Reduce the fraction by canceling out common factors:
   - The 3 in the numerator and denominator can be canceled out.

7. Final simplified expression:
   - 12x / 1

Therefore, the simplified expression is 12x.