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

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

Evaluate

$$\frac{x}{6-x}$$

Short Solution Steps

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

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

Since \frac{3\times 2}{2} and \frac{x}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2-x.

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

Divide x-3 by \frac{6-x}{2} by multiplying x-3 by the reciprocal of \frac{6-x}{2}.

$$1+\frac{\left(x-3\right)\times 2}{6-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6-x}{6-x}.

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

Since \frac{6-x}{6-x} and \frac{\left(x-3\right)\times 2}{6-x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 6-x+\left(x-3\right)\times 2.

$$\frac{6-x+2x-6}{6-x}$$

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

$$\frac{x}{6-x}$$

Expand

$$-\frac{x}{x-6}$$

Short Solution Steps

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

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

Since \frac{3\times 2}{2} and \frac{x}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2-x.

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

Divide x-3 by \frac{6-x}{2} by multiplying x-3 by the reciprocal of \frac{6-x}{2}.

$$1+\frac{\left(x-3\right)\times 2}{6-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6-x}{6-x}.

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

Since \frac{6-x}{6-x} and \frac{\left(x-3\right)\times 2}{6-x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 6-x+\left(x-3\right)\times 2.

$$\frac{6-x+2x-6}{6-x}$$

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

$$\frac{x}{6-x}$$