Solve (2)1500/a*1000+1200/frac{8a+240{a}}*1000=

$$( 2 ) \frac { 1500 } { a } \times 1000 + \frac { 1200 } { \frac { 8 a + 240 } { a } } \times 1000 =$$

Evaluate

$$\frac{150000\left(a^{2}+20a+600\right)}{a\left(a+30\right)}$$

Short Solution Steps

Multiply 2 and 1000 to get 2000.

$$2000\times \frac{1500}{a}+\frac{1200}{\frac{8a+240}{a}}\times 1000$$

Express 2000\times \frac{1500}{a} as a single fraction.

$$\frac{2000\times 1500}{a}+\frac{1200}{\frac{8a+240}{a}}\times 1000$$

Divide 1200 by \frac{8a+240}{a} by multiplying 1200 by the reciprocal of \frac{8a+240}{a}.

$$\frac{2000\times 1500}{a}+\frac{1200a}{8a+240}\times 1000$$

Factor the expressions that are not already factored in \frac{1200a}{8a+240}.

$$\frac{2000\times 1500}{a}+\frac{1200a}{8\left(a+30\right)}\times 1000$$

Cancel out 8 in both numerator and denominator.

$$\frac{2000\times 1500}{a}+\frac{150a}{a+30}\times 1000$$

Express \frac{150a}{a+30}\times 1000 as a single fraction.

$$\frac{2000\times 1500}{a}+\frac{150a\times 1000}{a+30}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and a+30 is a\left(a+30\right). Multiply \frac{2000\times 1500}{a} times \frac{a+30}{a+30}. Multiply \frac{150a\times 1000}{a+30} times \frac{a}{a}.

$$\frac{2000\times 1500\left(a+30\right)}{a\left(a+30\right)}+\frac{150a\times 1000a}{a\left(a+30\right)}$$

Since \frac{2000\times 1500\left(a+30\right)}{a\left(a+30\right)} and \frac{150a\times 1000a}{a\left(a+30\right)} have the same denominator, add them by adding their numerators.

$$\frac{2000\times 1500\left(a+30\right)+150a\times 1000a}{a\left(a+30\right)}$$

Do the multiplications in 2000\times 1500\left(a+30\right)+150a\times 1000a.

$$\frac{3000000a+90000000+150000a^{2}}{a\left(a+30\right)}$$

Expand a\left(a+30\right).

$$\frac{3000000a+90000000+150000a^{2}}{a^{2}+30a}$$

Expand

$$\frac{150000\left(a^{2}+20a+600\right)}{a\left(a+30\right)}$$

Short Solution Steps

Multiply 2 and 1000 to get 2000.

$$2000\times \frac{1500}{a}+\frac{1200}{\frac{8a+240}{a}}\times 1000$$

Express 2000\times \frac{1500}{a} as a single fraction.

$$\frac{2000\times 1500}{a}+\frac{1200}{\frac{8a+240}{a}}\times 1000$$

Divide 1200 by \frac{8a+240}{a} by multiplying 1200 by the reciprocal of \frac{8a+240}{a}.

$$\frac{2000\times 1500}{a}+\frac{1200a}{8a+240}\times 1000$$

Factor the expressions that are not already factored in \frac{1200a}{8a+240}.

$$\frac{2000\times 1500}{a}+\frac{1200a}{8\left(a+30\right)}\times 1000$$

Cancel out 8 in both numerator and denominator.

$$\frac{2000\times 1500}{a}+\frac{150a}{a+30}\times 1000$$

Express \frac{150a}{a+30}\times 1000 as a single fraction.

$$\frac{2000\times 1500}{a}+\frac{150a\times 1000}{a+30}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and a+30 is a\left(a+30\right). Multiply \frac{2000\times 1500}{a} times \frac{a+30}{a+30}. Multiply \frac{150a\times 1000}{a+30} times \frac{a}{a}.

$$\frac{2000\times 1500\left(a+30\right)}{a\left(a+30\right)}+\frac{150a\times 1000a}{a\left(a+30\right)}$$

Since \frac{2000\times 1500\left(a+30\right)}{a\left(a+30\right)} and \frac{150a\times 1000a}{a\left(a+30\right)} have the same denominator, add them by adding their numerators.

$$\frac{2000\times 1500\left(a+30\right)+150a\times 1000a}{a\left(a+30\right)}$$

Do the multiplications in 2000\times 1500\left(a+30\right)+150a\times 1000a.

$$\frac{3000000a+90000000+150000a^{2}}{a\left(a+30\right)}$$

Expand a\left(a+30\right).

$$\frac{3000000a+90000000+150000a^{2}}{a^{2}+30a}$$