Solve 4-3x/9-5/4-5/4--5-x/12+frac{x+3}{18}

$$\frac { 4 - 3 x } { 9 } \frac { - 5 } { 4 } - \frac { 5 } { 4 } - \frac { - 5 - x } { 12 } + \frac { x + 3 } { 18 }$$

Evaluate

$$\frac{5x-11}{9}$$

Short Solution Steps

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{4-3x}{9}\left(-\frac{5}{4}\right)-\frac{5}{4}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Multiply \frac{4-3x}{9} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(4-3x\right)\times 5}{9\times 4}-\frac{5}{4}-\frac{-5-x}{12}+\frac{x+3}{18}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9\times 4 and 4 is 4\times 9. Multiply \frac{5}{4} times \frac{9}{9}.

$$\frac{-\left(4-3x\right)\times 5}{4\times 9}-\frac{5\times 9}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Since \frac{-\left(4-3x\right)\times 5}{4\times 9} and \frac{5\times 9}{4\times 9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(4-3x\right)\times 5-5\times 9}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Do the multiplications in -\left(4-3x\right)\times 5-5\times 9.

$$\frac{-20+15x-45}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Combine like terms in -20+15x-45.

$$\frac{-65+15x}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\times 9 and 12 is 36. Multiply \frac{-5-x}{12} times \frac{3}{3}.

$$\frac{-65+15x}{36}-\frac{3\left(-5-x\right)}{36}+\frac{x+3}{18}$$

Since \frac{-65+15x}{36} and \frac{3\left(-5-x\right)}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-65+15x-3\left(-5-x\right)}{36}+\frac{x+3}{18}$$

Do the multiplications in -65+15x-3\left(-5-x\right).

$$\frac{-65+15x+15+3x}{36}+\frac{x+3}{18}$$

Combine like terms in -65+15x+15+3x.

$$\frac{-50+18x}{36}+\frac{x+3}{18}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 18 is 36. Multiply \frac{x+3}{18} times \frac{2}{2}.

$$\frac{-50+18x}{36}+\frac{2\left(x+3\right)}{36}$$

Since \frac{-50+18x}{36} and \frac{2\left(x+3\right)}{36} have the same denominator, add them by adding their numerators.

$$\frac{-50+18x+2\left(x+3\right)}{36}$$

Do the multiplications in -50+18x+2\left(x+3\right).

$$\frac{-50+18x+2x+6}{36}$$

Combine like terms in -50+18x+2x+6.

$$\frac{-44+20x}{36}$$

Expand

$$\frac{5x-11}{9}$$

Short Solution Steps

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{4-3x}{9}\left(-\frac{5}{4}\right)-\frac{5}{4}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Multiply \frac{4-3x}{9} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(4-3x\right)\times 5}{9\times 4}-\frac{5}{4}-\frac{-5-x}{12}+\frac{x+3}{18}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9\times 4 and 4 is 4\times 9. Multiply \frac{5}{4} times \frac{9}{9}.

$$\frac{-\left(4-3x\right)\times 5}{4\times 9}-\frac{5\times 9}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Since \frac{-\left(4-3x\right)\times 5}{4\times 9} and \frac{5\times 9}{4\times 9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(4-3x\right)\times 5-5\times 9}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Do the multiplications in -\left(4-3x\right)\times 5-5\times 9.

$$\frac{-20+15x-45}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

Combine like terms in -20+15x-45.

$$\frac{-65+15x}{4\times 9}-\frac{-5-x}{12}+\frac{x+3}{18}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\times 9 and 12 is 36. Multiply \frac{-5-x}{12} times \frac{3}{3}.

$$\frac{-65+15x}{36}-\frac{3\left(-5-x\right)}{36}+\frac{x+3}{18}$$

Since \frac{-65+15x}{36} and \frac{3\left(-5-x\right)}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-65+15x-3\left(-5-x\right)}{36}+\frac{x+3}{18}$$

Do the multiplications in -65+15x-3\left(-5-x\right).

$$\frac{-65+15x+15+3x}{36}+\frac{x+3}{18}$$

Combine like terms in -65+15x+15+3x.

$$\frac{-50+18x}{36}+\frac{x+3}{18}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 18 is 36. Multiply \frac{x+3}{18} times \frac{2}{2}.

$$\frac{-50+18x}{36}+\frac{2\left(x+3\right)}{36}$$

Since \frac{-50+18x}{36} and \frac{2\left(x+3\right)}{36} have the same denominator, add them by adding their numerators.

$$\frac{-50+18x+2\left(x+3\right)}{36}$$

Do the multiplications in -50+18x+2\left(x+3\right).

$$\frac{-50+18x+2x+6}{36}$$

Combine like terms in -50+18x+2x+6.

$$\frac{-44+20x}{36}$$