1 + {x^2 / (1 - x^2)

By multiplying the denominator by 1 I get the x squared to cancel out. But the book says the correct answer is (1 - x^2)^-1 I feel a little bit stupid but can't figure the algebra. But wolframalpha agrees with book answer.

Question

1 + {x^2 / (1 - x^2) 

By multiplying the denominator by 1 I get the x squared to cancel out. But the book says the correct answer is (1 - x^2)^-1 I feel a little bit stupid but can't figure the algebra. But wolframalpha agrees with book answer.

campbell_st · Answer

so the question is simplify 

$$1 + \frac{x^2}{(1 - x^2)}$$

is that correct..?

campbell_st · Answer

well rewrite 1 as 

$$\frac{1 - x^2}{1 - x^2} $$

which will give a common denominator so you will have

$$\frac{(1 - x^2) + x^2}{(1 - x^2)}$$

simplify the numerator will give 

$$\frac{1}{(1 - x^2)}$$

anonymous · Answer

Thanks