Solve 17/a+17-a/a-7+a^2+119/a^2+10a-119

$$\frac { 17 } { a + 17 } - \frac { a } { a - 7 } + \frac { a ^ { 2 } + 119 } { a ^ { 2 } + 10 a - 119 }$$

Evaluate

$$0$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+17 and a-7 is \left(a-7\right)\left(a+17\right). Multiply \frac{17}{a+17} times \frac{a-7}{a-7}. Multiply \frac{a}{a-7} times \frac{a+17}{a+17}.

$$\frac{17\left(a-7\right)}{\left(a-7\right)\left(a+17\right)}-\frac{a\left(a+17\right)}{\left(a-7\right)\left(a+17\right)}+\frac{a^{2}+119}{a^{2}+10a-119}$$

Since \frac{17\left(a-7\right)}{\left(a-7\right)\left(a+17\right)} and \frac{a\left(a+17\right)}{\left(a-7\right)\left(a+17\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17\left(a-7\right)-a\left(a+17\right)}{\left(a-7\right)\left(a+17\right)}+\frac{a^{2}+119}{a^{2}+10a-119}$$

Do the multiplications in 17\left(a-7\right)-a\left(a+17\right).

$$\frac{17a-119-a^{2}-17a}{\left(a-7\right)\left(a+17\right)}+\frac{a^{2}+119}{a^{2}+10a-119}$$

Combine like terms in 17a-119-a^{2}-17a.

$$\frac{-119-a^{2}}{\left(a-7\right)\left(a+17\right)}+\frac{a^{2}+119}{a^{2}+10a-119}$$

Factor a^{2}+10a-119.

$$\frac{-119-a^{2}}{\left(a-7\right)\left(a+17\right)}+\frac{a^{2}+119}{\left(a-7\right)\left(a+17\right)}$$

Since \frac{-119-a^{2}}{\left(a-7\right)\left(a+17\right)} and \frac{a^{2}+119}{\left(a-7\right)\left(a+17\right)} have the same denominator, add them by adding their numerators.

$$\frac{-119-a^{2}+a^{2}+119}{\left(a-7\right)\left(a+17\right)}$$

Combine like terms in -119-a^{2}+a^{2}+119.

$$\frac{0}{\left(a-7\right)\left(a+17\right)}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

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