Solve b+4/36+12b+b^2-3-2b/6+b

$$\frac { b + 4 } { 36 + 12 b + b ^ { 2 } } - \frac { 3 - 2 b } { 6 + b }$$

Evaluate

$$\frac{2\left(b^{2}+5b-7\right)}{\left(b+6\right)^{2}}$$

Short Solution Steps

Factor 36+12b+b^{2}.

$$\frac{b+4}{\left(b+6\right)^{2}}-\frac{3-2b}{6+b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b+6\right)^{2} and 6+b is \left(b+6\right)^{2}. Multiply \frac{3-2b}{6+b} times \frac{b+6}{b+6}.

$$\frac{b+4}{\left(b+6\right)^{2}}-\frac{\left(3-2b\right)\left(b+6\right)}{\left(b+6\right)^{2}}$$

Since \frac{b+4}{\left(b+6\right)^{2}} and \frac{\left(3-2b\right)\left(b+6\right)}{\left(b+6\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{b+4-\left(3-2b\right)\left(b+6\right)}{\left(b+6\right)^{2}}$$

Do the multiplications in b+4-\left(3-2b\right)\left(b+6\right).

$$\frac{b+4-3b-18+2b^{2}+12b}{\left(b+6\right)^{2}}$$

Combine like terms in b+4-3b-18+2b^{2}+12b.

$$\frac{10b-14+2b^{2}}{\left(b+6\right)^{2}}$$

Expand \left(b+6\right)^{2}.

$$\frac{10b-14+2b^{2}}{b^{2}+12b+36}$$

Expand

$$\frac{2\left(b^{2}+5b-7\right)}{\left(b+6\right)^{2}}$$

Short Solution Steps

Factor 36+12b+b^{2}.

$$\frac{b+4}{\left(b+6\right)^{2}}-\frac{3-2b}{6+b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b+6\right)^{2} and 6+b is \left(b+6\right)^{2}. Multiply \frac{3-2b}{6+b} times \frac{b+6}{b+6}.

$$\frac{b+4}{\left(b+6\right)^{2}}-\frac{\left(3-2b\right)\left(b+6\right)}{\left(b+6\right)^{2}}$$

Since \frac{b+4}{\left(b+6\right)^{2}} and \frac{\left(3-2b\right)\left(b+6\right)}{\left(b+6\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{b+4-\left(3-2b\right)\left(b+6\right)}{\left(b+6\right)^{2}}$$

Do the multiplications in b+4-\left(3-2b\right)\left(b+6\right).

$$\frac{b+4-3b-18+2b^{2}+12b}{\left(b+6\right)^{2}}$$

Combine like terms in b+4-3b-18+2b^{2}+12b.

$$\frac{10b-14+2b^{2}}{\left(b+6\right)^{2}}$$

Expand \left(b+6\right)^{2}.

$$\frac{10b-14+2b^{2}}{b^{2}+12b+36}$$