Solve 230/a+70+180/a+75

$$\frac { 230 } { a + 70 } + \frac { 180 } { a + 75 }$$

Evaluate

$$\frac{10\left(41a+2985\right)}{\left(a+70\right)\left(a+75\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+70 and a+75 is \left(a+70\right)\left(a+75\right). Multiply \frac{230}{a+70} times \frac{a+75}{a+75}. Multiply \frac{180}{a+75} times \frac{a+70}{a+70}.

$$\frac{230\left(a+75\right)}{\left(a+70\right)\left(a+75\right)}+\frac{180\left(a+70\right)}{\left(a+70\right)\left(a+75\right)}$$

Since \frac{230\left(a+75\right)}{\left(a+70\right)\left(a+75\right)} and \frac{180\left(a+70\right)}{\left(a+70\right)\left(a+75\right)} have the same denominator, add them by adding their numerators.

$$\frac{230\left(a+75\right)+180\left(a+70\right)}{\left(a+70\right)\left(a+75\right)}$$

Do the multiplications in 230\left(a+75\right)+180\left(a+70\right).

$$\frac{230a+17250+180a+12600}{\left(a+70\right)\left(a+75\right)}$$

Combine like terms in 230a+17250+180a+12600.

$$\frac{410a+29850}{\left(a+70\right)\left(a+75\right)}$$

Expand \left(a+70\right)\left(a+75\right).

$$\frac{410a+29850}{a^{2}+145a+5250}$$

Factor

$$\frac{10\left(41a+2985\right)}{\left(a+70\right)\left(a+75\right)}$$