Solve 2T(T+1/2T-1-3T/1+2)

$$2 T ( \frac { T + 1 } { 2 T - 1 } - \frac { 3 T } { 1 + 2 } )$$

Evaluate

$$\frac{2T\left(1+2T-2T^{2}\right)}{2T-1}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$2T\left(\frac{T+1}{2T-1}-\frac{3T}{3}\right)$$

Cancel out 3 and 3.

$$2T\left(\frac{T+1}{2T-1}-T\right)$$

Use the distributive property to multiply 2T by \frac{T+1}{2T-1}-T.

$$2T\times \frac{T+1}{2T-1}+2T\left(-T\right)$$

Express 2\times \frac{T+1}{2T-1} as a single fraction.

$$\frac{2\left(T+1\right)}{2T-1}T+2T\left(-T\right)$$

Express \frac{2\left(T+1\right)}{2T-1}T as a single fraction.

$$\frac{2\left(T+1\right)T}{2T-1}+2T\left(-1\right)T$$

Multiply T and T to get T^{2}.

$$\frac{2\left(T+1\right)T}{2T-1}+2T^{2}\left(-1\right)$$

Multiply 2 and -1 to get -2.

$$\frac{2\left(T+1\right)T}{2T-1}-2T^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2T^{2} times \frac{2T-1}{2T-1}.

$$\frac{2\left(T+1\right)T}{2T-1}+\frac{-2T^{2}\left(2T-1\right)}{2T-1}$$

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

$$\frac{2\left(T+1\right)T-2T^{2}\left(2T-1\right)}{2T-1}$$

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

$$\frac{2T^{2}+2T-4T^{3}+2T^{2}}{2T-1}$$

Combine like terms in 2T^{2}+2T-4T^{3}+2T^{2}.

$$\frac{4T^{2}+2T-4T^{3}}{2T-1}$$

Expand

$$-\frac{2\left(2T^{3}-2T^{2}-T\right)}{2T-1}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$2T\left(\frac{T+1}{2T-1}-\frac{3T}{3}\right)$$

Cancel out 3 and 3.

$$2T\left(\frac{T+1}{2T-1}-T\right)$$

Use the distributive property to multiply 2T by \frac{T+1}{2T-1}-T.

$$2T\times \frac{T+1}{2T-1}+2T\left(-T\right)$$

Express 2\times \frac{T+1}{2T-1} as a single fraction.

$$\frac{2\left(T+1\right)}{2T-1}T+2T\left(-T\right)$$

Express \frac{2\left(T+1\right)}{2T-1}T as a single fraction.

$$\frac{2\left(T+1\right)T}{2T-1}+2T\left(-1\right)T$$

Multiply T and T to get T^{2}.

$$\frac{2\left(T+1\right)T}{2T-1}+2T^{2}\left(-1\right)$$

Multiply 2 and -1 to get -2.

$$\frac{2\left(T+1\right)T}{2T-1}-2T^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2T^{2} times \frac{2T-1}{2T-1}.

$$\frac{2\left(T+1\right)T}{2T-1}+\frac{-2T^{2}\left(2T-1\right)}{2T-1}$$

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

$$\frac{2\left(T+1\right)T-2T^{2}\left(2T-1\right)}{2T-1}$$

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

$$\frac{2T^{2}+2T-4T^{3}+2T^{2}}{2T-1}$$

Combine like terms in 2T^{2}+2T-4T^{3}+2T^{2}.

$$\frac{4T^{2}+2T-4T^{3}}{2T-1}$$