Solve x/2left(3-xright)-x^2/7left(x-3right)^2

$$\frac{ x }{ 2 \left( 3-x \right) } - \frac{ { x }^{ 2 } }{ 7 { \left(x-3 \right) }^{ 2 } }$$

Evaluate

$$-\frac{3x\left(3x-7\right)}{14\left(3-x\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(3-x\right) and 7\left(x-3\right)^{2} is 14\left(x-3\right)^{2}. Multiply \frac{x}{2\left(3-x\right)} times \frac{-7\left(x-3\right)}{-7\left(x-3\right)}. Multiply \frac{x^{2}}{7\left(x-3\right)^{2}} times \frac{2}{2}.

$$\frac{x\left(-7\right)\left(x-3\right)}{14\left(x-3\right)^{2}}-\frac{2x^{2}}{14\left(x-3\right)^{2}}$$

Since \frac{x\left(-7\right)\left(x-3\right)}{14\left(x-3\right)^{2}} and \frac{2x^{2}}{14\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(-7\right)\left(x-3\right)-2x^{2}}{14\left(x-3\right)^{2}}$$

Do the multiplications in x\left(-7\right)\left(x-3\right)-2x^{2}.

$$\frac{-7x^{2}+21x-2x^{2}}{14\left(x-3\right)^{2}}$$

Combine like terms in -7x^{2}+21x-2x^{2}.

$$\frac{-9x^{2}+21x}{14\left(x-3\right)^{2}}$$

Expand 14\left(x-3\right)^{2}.

$$\frac{-9x^{2}+21x}{14x^{2}-84x+126}$$

Expand

$$-\frac{3\left(3x^{2}-7x\right)}{14\left(x-3\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(3-x\right) and 7\left(x-3\right)^{2} is 14\left(x-3\right)^{2}. Multiply \frac{x}{2\left(3-x\right)} times \frac{-7\left(x-3\right)}{-7\left(x-3\right)}. Multiply \frac{x^{2}}{7\left(x-3\right)^{2}} times \frac{2}{2}.

$$\frac{x\left(-7\right)\left(x-3\right)}{14\left(x-3\right)^{2}}-\frac{2x^{2}}{14\left(x-3\right)^{2}}$$

Since \frac{x\left(-7\right)\left(x-3\right)}{14\left(x-3\right)^{2}} and \frac{2x^{2}}{14\left(x-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(-7\right)\left(x-3\right)-2x^{2}}{14\left(x-3\right)^{2}}$$

Do the multiplications in x\left(-7\right)\left(x-3\right)-2x^{2}.

$$\frac{-7x^{2}+21x-2x^{2}}{14\left(x-3\right)^{2}}$$

Combine like terms in -7x^{2}+21x-2x^{2}.

$$\frac{-9x^{2}+21x}{14\left(x-3\right)^{2}}$$

Expand 14\left(x-3\right)^{2}.

$$\frac{-9x^{2}+21x}{14x^{2}-84x+126}$$