Solve x^2/4x^2+7x+3+3x/4x+3

$$\frac { x ^ { 2 } } { 4 x ^ { 2 } + 7 x + 3 } + \frac { 3 x } { 4 x + 3 }$$

Evaluate

$$\frac{x}{x+1}$$

Short Solution Steps

Factor 4x^{2}+7x+3.

$$\frac{x^{2}}{\left(x+1\right)\left(4x+3\right)}+\frac{3x}{4x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(4x+3\right) and 4x+3 is \left(x+1\right)\left(4x+3\right). Multiply \frac{3x}{4x+3} times \frac{x+1}{x+1}.

$$\frac{x^{2}}{\left(x+1\right)\left(4x+3\right)}+\frac{3x\left(x+1\right)}{\left(x+1\right)\left(4x+3\right)}$$

Since \frac{x^{2}}{\left(x+1\right)\left(4x+3\right)} and \frac{3x\left(x+1\right)}{\left(x+1\right)\left(4x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+3x\left(x+1\right)}{\left(x+1\right)\left(4x+3\right)}$$

Do the multiplications in x^{2}+3x\left(x+1\right).

$$\frac{x^{2}+3x^{2}+3x}{\left(x+1\right)\left(4x+3\right)}$$

Combine like terms in x^{2}+3x^{2}+3x.

$$\frac{4x^{2}+3x}{\left(x+1\right)\left(4x+3\right)}$$

Factor the expressions that are not already factored in \frac{4x^{2}+3x}{\left(x+1\right)\left(4x+3\right)}.

$$\frac{x\left(4x+3\right)}{\left(x+1\right)\left(4x+3\right)}$$

Cancel out 4x+3 in both numerator and denominator.

$$\frac{x}{x+1}$$

Factor

$$\frac{x}{x+1}$$