Solve 3*x+2/2x+1-1/2*frac{x+2{2x+1}+8}

$$\frac { 3 \cdot \frac { x + 2 } { 2 x + 1 } - 1 } { 2 \cdot \frac { x + 2 } { 2 x + 1 } + 8 }$$

Evaluate

$$\frac{x+5}{6\left(3x+2\right)}$$

Short Solution Steps

Express 3\times \frac{x+2}{2x+1} as a single fraction.

$$\frac{\frac{3\left(x+2\right)}{2x+1}-1}{2\times \frac{x+2}{2x+1}+8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2x+1}{2x+1}.

$$\frac{\frac{3\left(x+2\right)}{2x+1}-\frac{2x+1}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Since \frac{3\left(x+2\right)}{2x+1} and \frac{2x+1}{2x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3\left(x+2\right)-\left(2x+1\right)}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Do the multiplications in 3\left(x+2\right)-\left(2x+1\right).

$$\frac{\frac{3x+6-2x-1}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Combine like terms in 3x+6-2x-1.

$$\frac{\frac{x+5}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Express 2\times \frac{x+2}{2x+1} as a single fraction.

$$\frac{\frac{x+5}{2x+1}}{\frac{2\left(x+2\right)}{2x+1}+8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{2x+1}{2x+1}.

$$\frac{\frac{x+5}{2x+1}}{\frac{2\left(x+2\right)}{2x+1}+\frac{8\left(2x+1\right)}{2x+1}}$$

Since \frac{2\left(x+2\right)}{2x+1} and \frac{8\left(2x+1\right)}{2x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+5}{2x+1}}{\frac{2\left(x+2\right)+8\left(2x+1\right)}{2x+1}}$$

Do the multiplications in 2\left(x+2\right)+8\left(2x+1\right).

$$\frac{\frac{x+5}{2x+1}}{\frac{2x+4+16x+8}{2x+1}}$$

Combine like terms in 2x+4+16x+8.

$$\frac{\frac{x+5}{2x+1}}{\frac{18x+12}{2x+1}}$$

Divide \frac{x+5}{2x+1} by \frac{18x+12}{2x+1} by multiplying \frac{x+5}{2x+1} by the reciprocal of \frac{18x+12}{2x+1}.

$$\frac{\left(x+5\right)\left(2x+1\right)}{\left(2x+1\right)\left(18x+12\right)}$$

Cancel out 2x+1 in both numerator and denominator.

$$\frac{x+5}{18x+12}$$

Expand

$$\frac{x+5}{6\left(3x+2\right)}$$

Short Solution Steps

Express 3\times \frac{x+2}{2x+1} as a single fraction.

$$\frac{\frac{3\left(x+2\right)}{2x+1}-1}{2\times \frac{x+2}{2x+1}+8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2x+1}{2x+1}.

$$\frac{\frac{3\left(x+2\right)}{2x+1}-\frac{2x+1}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Since \frac{3\left(x+2\right)}{2x+1} and \frac{2x+1}{2x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3\left(x+2\right)-\left(2x+1\right)}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Do the multiplications in 3\left(x+2\right)-\left(2x+1\right).

$$\frac{\frac{3x+6-2x-1}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Combine like terms in 3x+6-2x-1.

$$\frac{\frac{x+5}{2x+1}}{2\times \frac{x+2}{2x+1}+8}$$

Express 2\times \frac{x+2}{2x+1} as a single fraction.

$$\frac{\frac{x+5}{2x+1}}{\frac{2\left(x+2\right)}{2x+1}+8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{2x+1}{2x+1}.

$$\frac{\frac{x+5}{2x+1}}{\frac{2\left(x+2\right)}{2x+1}+\frac{8\left(2x+1\right)}{2x+1}}$$

Since \frac{2\left(x+2\right)}{2x+1} and \frac{8\left(2x+1\right)}{2x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+5}{2x+1}}{\frac{2\left(x+2\right)+8\left(2x+1\right)}{2x+1}}$$

Do the multiplications in 2\left(x+2\right)+8\left(2x+1\right).

$$\frac{\frac{x+5}{2x+1}}{\frac{2x+4+16x+8}{2x+1}}$$

Combine like terms in 2x+4+16x+8.

$$\frac{\frac{x+5}{2x+1}}{\frac{18x+12}{2x+1}}$$

Divide \frac{x+5}{2x+1} by \frac{18x+12}{2x+1} by multiplying \frac{x+5}{2x+1} by the reciprocal of \frac{18x+12}{2x+1}.

$$\frac{\left(x+5\right)\left(2x+1\right)}{\left(2x+1\right)\left(18x+12\right)}$$

Cancel out 2x+1 in both numerator and denominator.

$$\frac{x+5}{18x+12}$$