Solve 4-3a/5-2b+5(a-10)/2b-5

$$4 - \frac { 3 a } { 5 - 2 b } + \frac { 5 ( a - 10 ) } { 2 b - 5 }$$

Evaluate

$$\frac{2\left(4a+4b-35\right)}{2b-5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{5-2b}{5-2b}.

$$\frac{4\left(5-2b\right)}{5-2b}-\frac{3a}{5-2b}+\frac{5\left(a-10\right)}{2b-5}$$

Since \frac{4\left(5-2b\right)}{5-2b} and \frac{3a}{5-2b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(5-2b\right)-3a}{5-2b}+\frac{5\left(a-10\right)}{2b-5}$$

Do the multiplications in 4\left(5-2b\right)-3a.

$$\frac{20-8b-3a}{5-2b}+\frac{5\left(a-10\right)}{2b-5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5-2b and 2b-5 is 2b-5. Multiply \frac{20-8b-3a}{5-2b} times \frac{-1}{-1}.

$$\frac{-\left(20-8b-3a\right)}{2b-5}+\frac{5\left(a-10\right)}{2b-5}$$

Since \frac{-\left(20-8b-3a\right)}{2b-5} and \frac{5\left(a-10\right)}{2b-5} have the same denominator, add them by adding their numerators.

$$\frac{-\left(20-8b-3a\right)+5\left(a-10\right)}{2b-5}$$

Do the multiplications in -\left(20-8b-3a\right)+5\left(a-10\right).

$$\frac{-20+8b+3a+5a-50}{2b-5}$$

Combine like terms in -20+8b+3a+5a-50.

$$\frac{-70+8b+8a}{2b-5}$$

Expand

$$\frac{2\left(4a+4b-35\right)}{2b-5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{5-2b}{5-2b}.

$$\frac{4\left(5-2b\right)}{5-2b}-\frac{3a}{5-2b}+\frac{5\left(a-10\right)}{2b-5}$$

Since \frac{4\left(5-2b\right)}{5-2b} and \frac{3a}{5-2b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(5-2b\right)-3a}{5-2b}+\frac{5\left(a-10\right)}{2b-5}$$

Do the multiplications in 4\left(5-2b\right)-3a.

$$\frac{20-8b-3a}{5-2b}+\frac{5\left(a-10\right)}{2b-5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5-2b and 2b-5 is 2b-5. Multiply \frac{20-8b-3a}{5-2b} times \frac{-1}{-1}.

$$\frac{-\left(20-8b-3a\right)}{2b-5}+\frac{5\left(a-10\right)}{2b-5}$$

Since \frac{-\left(20-8b-3a\right)}{2b-5} and \frac{5\left(a-10\right)}{2b-5} have the same denominator, add them by adding their numerators.

$$\frac{-\left(20-8b-3a\right)+5\left(a-10\right)}{2b-5}$$

Do the multiplications in -\left(20-8b-3a\right)+5\left(a-10\right).

$$\frac{-20+8b+3a+5a-50}{2b-5}$$

Combine like terms in -20+8b+3a+5a-50.

$$\frac{-70+8b+8a}{2b-5}$$