Solve (4x+5)(4x-1/3)/(x+9)(x-6)

$$\frac { ( 4 x + 5 ) ( 4 x - \frac { 1 } { 3 } ) } { ( x + 9 ) ( x - 6 ) }$$

Evaluate

$$\frac{\left(12x-1\right)\left(4x+5\right)}{3\left(x-6\right)\left(x+9\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of 4x+5 by each term of 4x-\frac{1}{3}.

$$\frac{16x^{2}+4x\left(-\frac{1}{3}\right)+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Express 4\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{16x^{2}+\frac{4\left(-1\right)}{3}x+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Multiply 4 and -1 to get -4.

$$\frac{16x^{2}+\frac{-4}{3}x+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{16x^{2}-\frac{4}{3}x+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Combine -\frac{4}{3}x and 20x to get \frac{56}{3}x.

$$\frac{16x^{2}+\frac{56}{3}x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Express 5\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{16x^{2}+\frac{56}{3}x+\frac{5\left(-1\right)}{3}}{\left(x+9\right)\left(x-6\right)}$$

Multiply 5 and -1 to get -5.

$$\frac{16x^{2}+\frac{56}{3}x+\frac{-5}{3}}{\left(x+9\right)\left(x-6\right)}$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$\frac{16x^{2}+\frac{56}{3}x-\frac{5}{3}}{\left(x+9\right)\left(x-6\right)}$$

Apply the distributive property by multiplying each term of x+9 by each term of x-6.

$$\frac{16x^{2}+\frac{56}{3}x-\frac{5}{3}}{x^{2}-6x+9x-54}$$

Combine -6x and 9x to get 3x.

$$\frac{16x^{2}+\frac{56}{3}x-\frac{5}{3}}{x^{2}+3x-54}$$

Expand

$$\frac{48x^{2}+56x-5}{3\left(x-6\right)\left(x+9\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of 4x+5 by each term of 4x-\frac{1}{3}.

$$\frac{16x^{2}+4x\left(-\frac{1}{3}\right)+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Express 4\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{16x^{2}+\frac{4\left(-1\right)}{3}x+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Multiply 4 and -1 to get -4.

$$\frac{16x^{2}+\frac{-4}{3}x+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{16x^{2}-\frac{4}{3}x+20x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Combine -\frac{4}{3}x and 20x to get \frac{56}{3}x.

$$\frac{16x^{2}+\frac{56}{3}x+5\left(-\frac{1}{3}\right)}{\left(x+9\right)\left(x-6\right)}$$

Express 5\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{16x^{2}+\frac{56}{3}x+\frac{5\left(-1\right)}{3}}{\left(x+9\right)\left(x-6\right)}$$

Multiply 5 and -1 to get -5.

$$\frac{16x^{2}+\frac{56}{3}x+\frac{-5}{3}}{\left(x+9\right)\left(x-6\right)}$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$\frac{16x^{2}+\frac{56}{3}x-\frac{5}{3}}{\left(x+9\right)\left(x-6\right)}$$

Apply the distributive property by multiplying each term of x+9 by each term of x-6.

$$\frac{16x^{2}+\frac{56}{3}x-\frac{5}{3}}{x^{2}-6x+9x-54}$$

Combine -6x and 9x to get 3x.

$$\frac{16x^{2}+\frac{56}{3}x-\frac{5}{3}}{x^{2}+3x-54}$$