Solve 4t^3/(t+1)-t^4/(t+1)^2

$$\frac { 4 t ^ { 3 } } { ( t + 1 ) } - \frac { t ^ { 4 } } { ( t + 1 ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t+1 and \left(t+1\right)^{2} is \left(t+1\right)^{2}. Multiply \frac{4t^{3}}{t+1} times \frac{t+1}{t+1}.

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

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

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

Do the multiplications in 4t^{3}\left(t+1\right)-t^{4}.

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

Combine like terms in 4t^{4}+4t^{3}-t^{4}.

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

Expand \left(t+1\right)^{2}.

$$\frac{3t^{4}+4t^{3}}{t^{2}+2t+1}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t+1 and \left(t+1\right)^{2} is \left(t+1\right)^{2}. Multiply \frac{4t^{3}}{t+1} times \frac{t+1}{t+1}.

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

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

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

Do the multiplications in 4t^{3}\left(t+1\right)-t^{4}.

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

Combine like terms in 4t^{4}+4t^{3}-t^{4}.

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

Expand \left(t+1\right)^{2}.

$$\frac{3t^{4}+4t^{3}}{t^{2}+2t+1}$$