Solve 7x/3y+6/7x/frac{7x{3y}+4/7x}

$$\frac { \frac { 7 x } { 3 y } + \frac { 6 } { 7 x } } { \frac { 7 x } { 3 y } + \frac { 4 } { 7 x } }$$

Evaluate

$$\frac{49x^{2}+18y}{49x^{2}+12y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 7x is 21xy. Multiply \frac{7x}{3y} times \frac{7x}{7x}. Multiply \frac{6}{7x} times \frac{3y}{3y}.

$$\frac{\frac{7x\times 7x}{21xy}+\frac{6\times 3y}{21xy}}{\frac{7x}{3y}+\frac{4}{7x}}$$

Since \frac{7x\times 7x}{21xy} and \frac{6\times 3y}{21xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x\times 7x+6\times 3y}{21xy}}{\frac{7x}{3y}+\frac{4}{7x}}$$

Do the multiplications in 7x\times 7x+6\times 3y.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{7x}{3y}+\frac{4}{7x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 7x is 21xy. Multiply \frac{7x}{3y} times \frac{7x}{7x}. Multiply \frac{4}{7x} times \frac{3y}{3y}.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{7x\times 7x}{21xy}+\frac{4\times 3y}{21xy}}$$

Since \frac{7x\times 7x}{21xy} and \frac{4\times 3y}{21xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{7x\times 7x+4\times 3y}{21xy}}$$

Do the multiplications in 7x\times 7x+4\times 3y.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{49x^{2}+12y}{21xy}}$$

Divide \frac{49x^{2}+18y}{21xy} by \frac{49x^{2}+12y}{21xy} by multiplying \frac{49x^{2}+18y}{21xy} by the reciprocal of \frac{49x^{2}+12y}{21xy}.

$$\frac{\left(49x^{2}+18y\right)\times 21xy}{21xy\left(49x^{2}+12y\right)}$$

Cancel out 21xy in both numerator and denominator.

$$\frac{49x^{2}+18y}{49x^{2}+12y}$$

Expand

$$\frac{49x^{2}+18y}{49x^{2}+12y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 7x is 21xy. Multiply \frac{7x}{3y} times \frac{7x}{7x}. Multiply \frac{6}{7x} times \frac{3y}{3y}.

$$\frac{\frac{7x\times 7x}{21xy}+\frac{6\times 3y}{21xy}}{\frac{7x}{3y}+\frac{4}{7x}}$$

Since \frac{7x\times 7x}{21xy} and \frac{6\times 3y}{21xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x\times 7x+6\times 3y}{21xy}}{\frac{7x}{3y}+\frac{4}{7x}}$$

Do the multiplications in 7x\times 7x+6\times 3y.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{7x}{3y}+\frac{4}{7x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 7x is 21xy. Multiply \frac{7x}{3y} times \frac{7x}{7x}. Multiply \frac{4}{7x} times \frac{3y}{3y}.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{7x\times 7x}{21xy}+\frac{4\times 3y}{21xy}}$$

Since \frac{7x\times 7x}{21xy} and \frac{4\times 3y}{21xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{7x\times 7x+4\times 3y}{21xy}}$$

Do the multiplications in 7x\times 7x+4\times 3y.

$$\frac{\frac{49x^{2}+18y}{21xy}}{\frac{49x^{2}+12y}{21xy}}$$

Divide \frac{49x^{2}+18y}{21xy} by \frac{49x^{2}+12y}{21xy} by multiplying \frac{49x^{2}+18y}{21xy} by the reciprocal of \frac{49x^{2}+12y}{21xy}.

$$\frac{\left(49x^{2}+18y\right)\times 21xy}{21xy\left(49x^{2}+12y\right)}$$

Cancel out 21xy in both numerator and denominator.

$$\frac{49x^{2}+18y}{49x^{2}+12y}$$