Solve 1+4/x+3/1+frac{9{x}}

$$\frac { 1 + \frac { 4 } { x + 3 } } { 1 + \frac { 9 } { x } }$$

Evaluate

$$\frac{x\left(x+7\right)}{\left(x+3\right)\left(x+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+3}{x+3}.

$$\frac{\frac{x+3}{x+3}+\frac{4}{x+3}}{1+\frac{9}{x}}$$

Since \frac{x+3}{x+3} and \frac{4}{x+3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+3+4}{x+3}}{1+\frac{9}{x}}$$

Combine like terms in x+3+4.

$$\frac{\frac{x+7}{x+3}}{1+\frac{9}{x}}$$

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

$$\frac{\frac{x+7}{x+3}}{\frac{x}{x}+\frac{9}{x}}$$

Since \frac{x}{x} and \frac{9}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+7}{x+3}}{\frac{x+9}{x}}$$

Divide \frac{x+7}{x+3} by \frac{x+9}{x} by multiplying \frac{x+7}{x+3} by the reciprocal of \frac{x+9}{x}.

$$\frac{\left(x+7\right)x}{\left(x+3\right)\left(x+9\right)}$$

Use the distributive property to multiply x+7 by x.

$$\frac{x^{2}+7x}{\left(x+3\right)\left(x+9\right)}$$

Apply the distributive property by multiplying each term of x+3 by each term of x+9.

$$\frac{x^{2}+7x}{x^{2}+9x+3x+27}$$

Combine 9x and 3x to get 12x.

$$\frac{x^{2}+7x}{x^{2}+12x+27}$$

Expand

$$\frac{x^{2}+7x}{\left(x+3\right)\left(x+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+3}{x+3}.

$$\frac{\frac{x+3}{x+3}+\frac{4}{x+3}}{1+\frac{9}{x}}$$

Since \frac{x+3}{x+3} and \frac{4}{x+3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+3+4}{x+3}}{1+\frac{9}{x}}$$

Combine like terms in x+3+4.

$$\frac{\frac{x+7}{x+3}}{1+\frac{9}{x}}$$

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

$$\frac{\frac{x+7}{x+3}}{\frac{x}{x}+\frac{9}{x}}$$

Since \frac{x}{x} and \frac{9}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+7}{x+3}}{\frac{x+9}{x}}$$

Divide \frac{x+7}{x+3} by \frac{x+9}{x} by multiplying \frac{x+7}{x+3} by the reciprocal of \frac{x+9}{x}.

$$\frac{\left(x+7\right)x}{\left(x+3\right)\left(x+9\right)}$$

Use the distributive property to multiply x+7 by x.

$$\frac{x^{2}+7x}{\left(x+3\right)\left(x+9\right)}$$

Apply the distributive property by multiplying each term of x+3 by each term of x+9.

$$\frac{x^{2}+7x}{x^{2}+9x+3x+27}$$

Combine 9x and 3x to get 12x.

$$\frac{x^{2}+7x}{x^{2}+12x+27}$$