Solve -12/7-sqrt{-1}=

$$\frac { - 12 } { 7 - \sqrt { - 1 } } =$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Rationalize the denominator of \frac{-12}{7-\sqrt{-1}} by multiplying numerator and denominator by 7+\sqrt{-1}.

$$\frac{-12\left(7+\sqrt{-1}\right)}{\left(7-\sqrt{-1}\right)\left(7+\sqrt{-1}\right)}$$

Consider \left(7-\sqrt{-1}\right)\left(7+\sqrt{-1}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-12\left(7+\sqrt{-1}\right)}{7^{2}-\left(\sqrt{-1}\right)^{2}}$$

Square 7. Square \sqrt{-1}.

$$\frac{-12\left(7+\sqrt{-1}\right)}{49+1}$$

Subtract -1 from 49 to get 50.

$$\frac{-12\left(7+\sqrt{-1}\right)}{50}$$

Divide -12\left(7+\sqrt{-1}\right) by 50 to get -\frac{6}{25}\left(7+\sqrt{-1}\right).

$$-\frac{6}{25}\left(7+\sqrt{-1}\right)$$

Use the distributive property to multiply -\frac{6}{25} by 7+\sqrt{-1}.

$$-\frac{6}{25}\times 7-\frac{6}{25}\sqrt{-1}$$

Express -\frac{6}{25}\times 7 as a single fraction.

$$\frac{-6\times 7}{25}-\frac{6}{25}\sqrt{-1}$$

Multiply -6 and 7 to get -42.

$$\frac{-42}{25}-\frac{6}{25}\sqrt{-1}$$

Fraction \frac{-42}{25} can be rewritten as -\frac{42}{25} by extracting the negative sign.

$$-\frac{42}{25}-\frac{6}{25}\sqrt{-1}$$