Solve (3a-2):(a+3)+(a-4)*(1-3a)

$$( 3 a - 2 ) : ( a + 3 ) + ( a - 4 ) \times ( 1 - 3 a )$$

Evaluate

$$\frac{-3a^{3}+4a^{2}+38a-14}{a+3}$$

Short Solution Steps

Apply the distributive property by multiplying each term of a-4 by each term of 1-3a.

$$\frac{3a-2}{a+3}+a-3a^{2}-4+12a$$

Combine a and 12a to get 13a.

$$\frac{3a-2}{a+3}+13a-3a^{2}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 13a-3a^{2}-4 times \frac{a+3}{a+3}.

$$\frac{3a-2}{a+3}+\frac{\left(13a-3a^{2}-4\right)\left(a+3\right)}{a+3}$$

Since \frac{3a-2}{a+3} and \frac{\left(13a-3a^{2}-4\right)\left(a+3\right)}{a+3} have the same denominator, add them by adding their numerators.

$$\frac{3a-2+\left(13a-3a^{2}-4\right)\left(a+3\right)}{a+3}$$

Do the multiplications in 3a-2+\left(13a-3a^{2}-4\right)\left(a+3\right).

$$\frac{3a-2+13a^{2}+39a-3a^{3}-9a^{2}-4a-12}{a+3}$$

Combine like terms in 3a-2+13a^{2}+39a-3a^{3}-9a^{2}-4a-12.

$$\frac{38a-14+4a^{2}-3a^{3}}{a+3}$$

Expand

$$\frac{-3a^{3}+4a^{2}+38a-14}{a+3}$$

Short Solution Steps

Apply the distributive property by multiplying each term of a-4 by each term of 1-3a.

$$\frac{3a-2}{a+3}+a-3a^{2}-4+12a$$

Combine a and 12a to get 13a.

$$\frac{3a-2}{a+3}+13a-3a^{2}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 13a-3a^{2}-4 times \frac{a+3}{a+3}.

$$\frac{3a-2}{a+3}+\frac{\left(13a-3a^{2}-4\right)\left(a+3\right)}{a+3}$$

Since \frac{3a-2}{a+3} and \frac{\left(13a-3a^{2}-4\right)\left(a+3\right)}{a+3} have the same denominator, add them by adding their numerators.

$$\frac{3a-2+\left(13a-3a^{2}-4\right)\left(a+3\right)}{a+3}$$

Do the multiplications in 3a-2+\left(13a-3a^{2}-4\right)\left(a+3\right).

$$\frac{3a-2+13a^{2}+39a-3a^{3}-9a^{2}-4a-12}{a+3}$$

Combine like terms in 3a-2+13a^{2}+39a-3a^{3}-9a^{2}-4a-12.

$$\frac{38a-14+4a^{2}-3a^{3}}{a+3}$$