Solve 4-2(2x+3/9+3x)/3+5(frac{2x+3{4+3x})}

$$\frac { 4 - 2 ( \frac { 2 x + 3 } { 9 + 3 x } ) } { 3 + 5 ( \frac { 2 x + 3 } { 4 + 3 x } ) }$$

Evaluate

$$\frac{2\left(3x+4\right)\left(4x+15\right)}{3\left(x+3\right)\left(19x+27\right)}$$

Short Solution Steps

Express 2\times \frac{2x+3}{9+3x} as a single fraction.

$$\frac{4-\frac{2\left(2x+3\right)}{9+3x}}{3+5\times \frac{2x+3}{4+3x}}$$

Factor 9+3x.

$$\frac{4-\frac{2\left(2x+3\right)}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{3\left(x+3\right)}{3\left(x+3\right)}.

$$\frac{\frac{4\times 3\left(x+3\right)}{3\left(x+3\right)}-\frac{2\left(2x+3\right)}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

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

$$\frac{\frac{4\times 3\left(x+3\right)-2\left(2x+3\right)}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

Do the multiplications in 4\times 3\left(x+3\right)-2\left(2x+3\right).

$$\frac{\frac{12x+36-4x-6}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

Combine like terms in 12x+36-4x-6.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

Express 5\times \frac{2x+3}{4+3x} as a single fraction.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{3+\frac{5\left(2x+3\right)}{4+3x}}$$

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

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{3\left(4+3x\right)}{4+3x}+\frac{5\left(2x+3\right)}{4+3x}}$$

Since \frac{3\left(4+3x\right)}{4+3x} and \frac{5\left(2x+3\right)}{4+3x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{3\left(4+3x\right)+5\left(2x+3\right)}{4+3x}}$$

Do the multiplications in 3\left(4+3x\right)+5\left(2x+3\right).

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{12+9x+10x+15}{4+3x}}$$

Combine like terms in 12+9x+10x+15.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{27+19x}{4+3x}}$$

Divide \frac{8x+30}{3\left(x+3\right)} by \frac{27+19x}{4+3x} by multiplying \frac{8x+30}{3\left(x+3\right)} by the reciprocal of \frac{27+19x}{4+3x}.

$$\frac{\left(8x+30\right)\left(4+3x\right)}{3\left(x+3\right)\left(27+19x\right)}$$

Apply the distributive property by multiplying each term of 8x+30 by each term of 4+3x.

$$\frac{32x+24x^{2}+120+90x}{3\left(x+3\right)\left(27+19x\right)}$$

Combine 32x and 90x to get 122x.

$$\frac{122x+24x^{2}+120}{3\left(x+3\right)\left(27+19x\right)}$$

Use the distributive property to multiply 3 by x+3.

$$\frac{122x+24x^{2}+120}{\left(3x+9\right)\left(27+19x\right)}$$

Apply the distributive property by multiplying each term of 3x+9 by each term of 27+19x.

$$\frac{122x+24x^{2}+120}{81x+57x^{2}+243+171x}$$

Combine 81x and 171x to get 252x.

$$\frac{122x+24x^{2}+120}{252x+57x^{2}+243}$$

Expand

$$\frac{2\left(12x^{2}+61x+60\right)}{3\left(x+3\right)\left(19x+27\right)}$$

Short Solution Steps

Express 2\times \frac{2x+3}{9+3x} as a single fraction.

$$\frac{4-\frac{2\left(2x+3\right)}{9+3x}}{3+5\times \frac{2x+3}{4+3x}}$$

Factor 9+3x.

$$\frac{4-\frac{2\left(2x+3\right)}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{3\left(x+3\right)}{3\left(x+3\right)}.

$$\frac{\frac{4\times 3\left(x+3\right)}{3\left(x+3\right)}-\frac{2\left(2x+3\right)}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

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

$$\frac{\frac{4\times 3\left(x+3\right)-2\left(2x+3\right)}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

Do the multiplications in 4\times 3\left(x+3\right)-2\left(2x+3\right).

$$\frac{\frac{12x+36-4x-6}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

Combine like terms in 12x+36-4x-6.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{3+5\times \frac{2x+3}{4+3x}}$$

Express 5\times \frac{2x+3}{4+3x} as a single fraction.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{3+\frac{5\left(2x+3\right)}{4+3x}}$$

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

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{3\left(4+3x\right)}{4+3x}+\frac{5\left(2x+3\right)}{4+3x}}$$

Since \frac{3\left(4+3x\right)}{4+3x} and \frac{5\left(2x+3\right)}{4+3x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{3\left(4+3x\right)+5\left(2x+3\right)}{4+3x}}$$

Do the multiplications in 3\left(4+3x\right)+5\left(2x+3\right).

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{12+9x+10x+15}{4+3x}}$$

Combine like terms in 12+9x+10x+15.

$$\frac{\frac{8x+30}{3\left(x+3\right)}}{\frac{27+19x}{4+3x}}$$

Divide \frac{8x+30}{3\left(x+3\right)} by \frac{27+19x}{4+3x} by multiplying \frac{8x+30}{3\left(x+3\right)} by the reciprocal of \frac{27+19x}{4+3x}.

$$\frac{\left(8x+30\right)\left(4+3x\right)}{3\left(x+3\right)\left(27+19x\right)}$$

Apply the distributive property by multiplying each term of 8x+30 by each term of 4+3x.

$$\frac{32x+24x^{2}+120+90x}{3\left(x+3\right)\left(27+19x\right)}$$

Combine 32x and 90x to get 122x.

$$\frac{122x+24x^{2}+120}{3\left(x+3\right)\left(27+19x\right)}$$

Use the distributive property to multiply 3 by x+3.

$$\frac{122x+24x^{2}+120}{\left(3x+9\right)\left(27+19x\right)}$$

Apply the distributive property by multiplying each term of 3x+9 by each term of 27+19x.

$$\frac{122x+24x^{2}+120}{81x+57x^{2}+243+171x}$$

Combine 81x and 171x to get 252x.

$$\frac{122x+24x^{2}+120}{252x+57x^{2}+243}$$