Rewrite rational expressions. Show all work and circle your answers.

Question

([j-1]/j)/([j^2-1]/j^2) in other words it is a fraction over a fraction. the numerator of the fraction on top is j-1 and the denominator is j. this fraction is on top of the fraction with the numerator being j^2-1 over the denominator j^2. Thank you for your assistence. also the paranthesis aren't actually there, i was just trying to show what terms were put together.

Answer 1

([j-1]/j)/([j^2-1]/j^2)

 

1. change the division problem into a multiplication problem by reciprocal of the denominator fraction

(j-1)/j   x   j²/(j²-1)

 

2. multiple the numerators together and the denominators together

[(j-1) x j²] / [j x (j²-1)]

 

3. you can cross out one j from the top and bottom

[(j-1) x j] / [1 x (j²-1)]

 

4. rewrite j² -1 into (j-1)(j+1)

[(j-1) x j] / [(j-1)(j+1)]

 

5. you can cross out j-1 from the top and bottom

j/(j+1)