Expert Answer to "For Exercise, solve the equation. 48m2−4m+3=12m−4"

alka8q7

Answered question

2021-11-17

For Exercise, solve the equation.

\frac{48}{m^{2} - 4 m} + 3 = \frac{12}{m - 4}

Annie Midgett

Beginner2021-11-18Added 7 answers

Step 1
We factor the denominators

\frac{48}{m^{2} - 4 m} + 3 = \frac{12}{m - 4}

\frac{48}{m (m - 4)} + 3 = \frac{12}{m - 4}

LCD is

m (m - 4)

Then we multiply both sides by LCD so that we get rid of the fractions

\frac{48}{m (m - 4)} + 3 = \frac{12}{m - 4}

m (m - 4) [\frac{48}{m (m - 4)} + 3] = m (m - 4) \frac{12}{m - 4}

48 + 3 m (m - 4) = 12 m

Step 2
Then distribute 3m, combine the like terms and then make right side equal to 0.
Then factor

48 + 3 m (m - 4) = 12 m

48 + 3 m^{2} - 12 m = 12 m

3 m^{2} - 24 m + 48 = 0

3 (m^{2} - 8 m + 16) = 0

3 (m - 4) (m - 4) = 0

3 {(m - 4)}^{2} = 0

Set each factor equal to 0 and solve for m

m - 4 = 0

m = 4

For

m = 4

we get denominator equal to 0 in the original equation. So

m = 4

can not be a solution
Answer: No solution

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?