Solve -(m-3)(m-1)/1-m+3/3

$$\frac { - ( m - 3 ) ( m - 1 ) } { 1 } - \frac { m + 3 } { 3 }$$

Evaluate

$$-m^{2}+\frac{11m}{3}-4$$

Short Solution Steps

To find the opposite of m-3, find the opposite of each term.

$$\frac{\left(-m-\left(-3\right)\right)\left(m-1\right)}{1}-\frac{m+3}{3}$$

The opposite of -3 is 3.

$$\frac{\left(-m+3\right)\left(m-1\right)}{1}-\frac{m+3}{3}$$

Anything divided by one gives itself.

$$\left(-m+3\right)\left(m-1\right)-\frac{m+3}{3}$$

Apply the distributive property by multiplying each term of -m+3 by each term of m-1.

$$-m^{2}+m+3m-3-\frac{m+3}{3}$$

Combine m and 3m to get 4m.

$$-m^{2}+4m-3-\frac{m+3}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -m^{2}+4m-3 times \frac{3}{3}.

$$\frac{3\left(-m^{2}+4m-3\right)}{3}-\frac{m+3}{3}$$

Since \frac{3\left(-m^{2}+4m-3\right)}{3} and \frac{m+3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-m^{2}+4m-3\right)-\left(m+3\right)}{3}$$

Do the multiplications in 3\left(-m^{2}+4m-3\right)-\left(m+3\right).

$$\frac{-3m^{2}+12m-9-m-3}{3}$$

Combine like terms in -3m^{2}+12m-9-m-3.

$$\frac{-3m^{2}+11m-12}{3}$$

Expand

$$-m^{2}+\frac{11m}{3}-4$$

Short Solution Steps

To find the opposite of m-3, find the opposite of each term.

$$\frac{\left(-m-\left(-3\right)\right)\left(m-1\right)}{1}-\frac{m+3}{3}$$

The opposite of -3 is 3.

$$\frac{\left(-m+3\right)\left(m-1\right)}{1}-\frac{m+3}{3}$$

Anything divided by one gives itself.

$$\left(-m+3\right)\left(m-1\right)-\frac{m+3}{3}$$

Apply the distributive property by multiplying each term of -m+3 by each term of m-1.

$$-m^{2}+m+3m-3-\frac{m+3}{3}$$

Combine m and 3m to get 4m.

$$-m^{2}+4m-3-\frac{m+3}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -m^{2}+4m-3 times \frac{3}{3}.

$$\frac{3\left(-m^{2}+4m-3\right)}{3}-\frac{m+3}{3}$$

Since \frac{3\left(-m^{2}+4m-3\right)}{3} and \frac{m+3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-m^{2}+4m-3\right)-\left(m+3\right)}{3}$$

Do the multiplications in 3\left(-m^{2}+4m-3\right)-\left(m+3\right).

$$\frac{-3m^{2}+12m-9-m-3}{3}$$

Combine like terms in -3m^{2}+12m-9-m-3.

$$\frac{-3m^{2}+11m-12}{3}$$