Solve 4/3+2x/5-3/4(5/12-frac{7x}{6})-frac{5}{3}(frac{4x}{15}-frac{3}{10})-frac{6}{5}

$$\frac { 4 } { 3 } + \frac { 2 x } { 5 } - \frac { 3 } { 4 } ( \frac { 5 } { 12 } - \frac { 7 x } { 6 } ) - \frac { 5 } { 3 } ( \frac { 4 x } { 15 } - \frac { 3 } { 10 } ) - \frac { 6 } { 5 }$$

Evaluate

$$\frac{299x}{360}+\frac{77}{240}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{4}{3} times \frac{5}{5}. Multiply \frac{2x}{5} times \frac{3}{3}.

$$\frac{4\times 5}{15}+\frac{3\times 2x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{7x}{6}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Since \frac{4\times 5}{15} and \frac{3\times 2x}{15} have the same denominator, add them by adding their numerators.

$$\frac{4\times 5+3\times 2x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{7x}{6}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Do the multiplications in 4\times 5+3\times 2x.

$$\frac{20+6x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{7x}{6}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 6 is 12. Multiply \frac{7x}{6} times \frac{2}{2}.

$$\frac{20+6x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{2\times 7x}{12}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Since \frac{5}{12} and \frac{2\times 7x}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20+6x}{15}-\frac{3}{4}\times \frac{5-2\times 7x}{12}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Do the multiplications in 5-2\times 7x.

$$\frac{20+6x}{15}-\frac{3}{4}\times \frac{5-14x}{12}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Multiply \frac{3}{4} times \frac{5-14x}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20+6x}{15}-\frac{3\left(5-14x\right)}{4\times 12}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{20+6x}{15}-\frac{-14x+5}{4\times 4}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Multiply 4 and 4 to get 16.

$$\frac{20+6x}{15}-\frac{-14x+5}{16}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 16 is 240. Multiply \frac{20+6x}{15} times \frac{16}{16}. Multiply \frac{-14x+5}{16} times \frac{15}{15}.

$$\frac{16\left(20+6x\right)}{240}-\frac{15\left(-14x+5\right)}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Since \frac{16\left(20+6x\right)}{240} and \frac{15\left(-14x+5\right)}{240} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16\left(20+6x\right)-15\left(-14x+5\right)}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Do the multiplications in 16\left(20+6x\right)-15\left(-14x+5\right).

$$\frac{320+96x+210x-75}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Combine like terms in 320+96x+210x-75.

$$\frac{245+306x}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 10 is 30. Multiply \frac{4x}{15} times \frac{2}{2}. Multiply \frac{3}{10} times \frac{3}{3}.

$$\frac{245+306x}{240}-\frac{5}{3}\left(\frac{2\times 4x}{30}-\frac{3\times 3}{30}\right)-\frac{6}{5}$$

Since \frac{2\times 4x}{30} and \frac{3\times 3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{245+306x}{240}-\frac{5}{3}\times \frac{2\times 4x-3\times 3}{30}-\frac{6}{5}$$

Do the multiplications in 2\times 4x-3\times 3.

$$\frac{245+306x}{240}-\frac{5}{3}\times \frac{8x-9}{30}-\frac{6}{5}$$

Multiply \frac{5}{3} times \frac{8x-9}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{245+306x}{240}-\frac{5\left(8x-9\right)}{3\times 30}-\frac{6}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{245+306x}{240}-\frac{8x-9}{3\times 6}-\frac{6}{5}$$

Multiply 3 and 6 to get 18.

$$\frac{245+306x}{240}-\frac{8x-9}{18}-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 240 and 18 is 720. Multiply \frac{245+306x}{240} times \frac{3}{3}. Multiply \frac{8x-9}{18} times \frac{40}{40}.

$$\frac{3\left(245+306x\right)}{720}-\frac{40\left(8x-9\right)}{720}-\frac{6}{5}$$

Since \frac{3\left(245+306x\right)}{720} and \frac{40\left(8x-9\right)}{720} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(245+306x\right)-40\left(8x-9\right)}{720}-\frac{6}{5}$$

Do the multiplications in 3\left(245+306x\right)-40\left(8x-9\right).

$$\frac{735+918x-320x+360}{720}-\frac{6}{5}$$

Combine like terms in 735+918x-320x+360.

$$\frac{1095+598x}{720}-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 720 and 5 is 720. Multiply \frac{6}{5} times \frac{144}{144}.

$$\frac{1095+598x}{720}-\frac{6\times 144}{720}$$

Since \frac{1095+598x}{720} and \frac{6\times 144}{720} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1095+598x-6\times 144}{720}$$

Do the multiplications in 1095+598x-6\times 144.

$$\frac{1095+598x-864}{720}$$

Combine like terms in 1095+598x-864.

$$\frac{231+598x}{720}$$

Expand

$$\frac{299x}{360}+\frac{77}{240}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{4}{3} times \frac{5}{5}. Multiply \frac{2x}{5} times \frac{3}{3}.

$$\frac{4\times 5}{15}+\frac{3\times 2x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{7x}{6}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Since \frac{4\times 5}{15} and \frac{3\times 2x}{15} have the same denominator, add them by adding their numerators.

$$\frac{4\times 5+3\times 2x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{7x}{6}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Do the multiplications in 4\times 5+3\times 2x.

$$\frac{20+6x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{7x}{6}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 6 is 12. Multiply \frac{7x}{6} times \frac{2}{2}.

$$\frac{20+6x}{15}-\frac{3}{4}\left(\frac{5}{12}-\frac{2\times 7x}{12}\right)-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Since \frac{5}{12} and \frac{2\times 7x}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20+6x}{15}-\frac{3}{4}\times \frac{5-2\times 7x}{12}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Do the multiplications in 5-2\times 7x.

$$\frac{20+6x}{15}-\frac{3}{4}\times \frac{5-14x}{12}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Multiply \frac{3}{4} times \frac{5-14x}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20+6x}{15}-\frac{3\left(5-14x\right)}{4\times 12}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{20+6x}{15}-\frac{-14x+5}{4\times 4}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Multiply 4 and 4 to get 16.

$$\frac{20+6x}{15}-\frac{-14x+5}{16}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 16 is 240. Multiply \frac{20+6x}{15} times \frac{16}{16}. Multiply \frac{-14x+5}{16} times \frac{15}{15}.

$$\frac{16\left(20+6x\right)}{240}-\frac{15\left(-14x+5\right)}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Since \frac{16\left(20+6x\right)}{240} and \frac{15\left(-14x+5\right)}{240} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16\left(20+6x\right)-15\left(-14x+5\right)}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Do the multiplications in 16\left(20+6x\right)-15\left(-14x+5\right).

$$\frac{320+96x+210x-75}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

Combine like terms in 320+96x+210x-75.

$$\frac{245+306x}{240}-\frac{5}{3}\left(\frac{4x}{15}-\frac{3}{10}\right)-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 10 is 30. Multiply \frac{4x}{15} times \frac{2}{2}. Multiply \frac{3}{10} times \frac{3}{3}.

$$\frac{245+306x}{240}-\frac{5}{3}\left(\frac{2\times 4x}{30}-\frac{3\times 3}{30}\right)-\frac{6}{5}$$

Since \frac{2\times 4x}{30} and \frac{3\times 3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{245+306x}{240}-\frac{5}{3}\times \frac{2\times 4x-3\times 3}{30}-\frac{6}{5}$$

Do the multiplications in 2\times 4x-3\times 3.

$$\frac{245+306x}{240}-\frac{5}{3}\times \frac{8x-9}{30}-\frac{6}{5}$$

Multiply \frac{5}{3} times \frac{8x-9}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{245+306x}{240}-\frac{5\left(8x-9\right)}{3\times 30}-\frac{6}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{245+306x}{240}-\frac{8x-9}{3\times 6}-\frac{6}{5}$$

Multiply 3 and 6 to get 18.

$$\frac{245+306x}{240}-\frac{8x-9}{18}-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 240 and 18 is 720. Multiply \frac{245+306x}{240} times \frac{3}{3}. Multiply \frac{8x-9}{18} times \frac{40}{40}.

$$\frac{3\left(245+306x\right)}{720}-\frac{40\left(8x-9\right)}{720}-\frac{6}{5}$$

Since \frac{3\left(245+306x\right)}{720} and \frac{40\left(8x-9\right)}{720} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(245+306x\right)-40\left(8x-9\right)}{720}-\frac{6}{5}$$

Do the multiplications in 3\left(245+306x\right)-40\left(8x-9\right).

$$\frac{735+918x-320x+360}{720}-\frac{6}{5}$$

Combine like terms in 735+918x-320x+360.

$$\frac{1095+598x}{720}-\frac{6}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 720 and 5 is 720. Multiply \frac{6}{5} times \frac{144}{144}.

$$\frac{1095+598x}{720}-\frac{6\times 144}{720}$$

Since \frac{1095+598x}{720} and \frac{6\times 144}{720} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1095+598x-6\times 144}{720}$$

Do the multiplications in 1095+598x-6\times 144.

$$\frac{1095+598x-864}{720}$$

Combine like terms in 1095+598x-864.

$$\frac{231+598x}{720}$$