Solve 7x/2y-49x^2+4y^2/14xy+2y-49x/7x

$$\frac{ 7x }{ 2y } - \frac{ 49 { x }^{ 2 } +4 { y }^{ 2 } }{ 14xy } + \frac{ 2y-49x }{ 7x }$$

Evaluate

$$-7$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2y and 14xy is 14xy. Multiply \frac{7x}{2y} times \frac{7x}{7x}.

$$\frac{7x\times 7x}{14xy}-\frac{49x^{2}+4y^{2}}{14xy}+\frac{2y-49x}{7x}$$

Since \frac{7x\times 7x}{14xy} and \frac{49x^{2}+4y^{2}}{14xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7x\times 7x-\left(49x^{2}+4y^{2}\right)}{14xy}+\frac{2y-49x}{7x}$$

Do the multiplications in 7x\times 7x-\left(49x^{2}+4y^{2}\right).

$$\frac{49x^{2}-49x^{2}-4y^{2}}{14xy}+\frac{2y-49x}{7x}$$

Combine like terms in 49x^{2}-49x^{2}-4y^{2}.

$$\frac{-4y^{2}}{14xy}+\frac{2y-49x}{7x}$$

Cancel out 2y in both numerator and denominator.

$$\frac{-2y}{7x}+\frac{2y-49x}{7x}$$

Since \frac{-2y}{7x} and \frac{2y-49x}{7x} have the same denominator, add them by adding their numerators.

$$\frac{-2y+2y-49x}{7x}$$

Combine like terms in -2y+2y-49x.

$$\frac{-49x}{7x}$$

Cancel out 7x in both numerator and denominator.

$$-7$$

Factor

$$-7$$