SOLUTION: {{{(x^-2 - y^-2)^-1}}} I am have trouble with this rational expression. Would you help me please. Also I am having trouble with {{{(1/x + 1/2) * (4/x^2 - 1)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(x^-2 - y^-2)^-1}}} I am have trouble with this rational expression. Would you help me please. Also I am having trouble with {{{(1/x + 1/2) * (4/x^2 - 1)}}}       Log On


   

Question 109900: %28x%5E-2+-+y%5E-2%29%5E-1 I am have trouble with this rational expression. Would you help me please. Also I am having trouble with %281%2Fx+%2B+1%2F2%29+%2A+%284%2Fx%5E2+-+1%29
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E-2+-+y%5E-2%29%5E-1

%281%2Fx%5E2+-+1%2Fy%5E2%29%5E-1
1%2F%28%281%2Fx%5E2+-+1%2Fy%5E2%29%29
1%2F%28%281%2Ay%5E2+-+1%2Ax%5E2%29%2F%28y%5E2%2Ax%5E2%29%29

%281%2F1%29%2F%28%28y%5E2+-+x%5E2%29%2F%28y%5E2%2Ax%5E2%29%29...multiply inner and outer terms

%28y%5E2%2Ax%5E2%29%2F%28y%5E2+-+x%5E2%29...

2.
%281%2Fx+%2B+1%2F2%29+%2A+%284%2Fx%5E2+-+1%2F1%29
%28%281%2A2+%2B+1%2Ax%29%2F2x%29+%2A+%28%284+-+x%5E2%29%2Fx%5E2%29%29
%28%282+%2B+x%29%2F2x%29+%2A+%28%284+-+x%5E2%29%2Fx%5E2%29%29.........multiply nominator by nominator, and denominator by denominator
%28%282+%2B+x%29%284+-+x%5E2%29%2F%282x+%2Ax%5E2%29%29.........%284+-+x%5E2%29=%282-x%29%282%2Bx%29

%28%282+%2B+x%29%282-x%29%282%2Bx%29%29%2F%282+%2Ax%5E3%29%29.........