( 1 / ( 1 + ( 1 / x^2 ) ) ) * (1 / x) = x / (x^2 + 1)
True or False?
If I put the LHS into my calculator it comes out with the RHS, but I can't do it by hand.
When I do it by hand I get:
1 / (x^2 + x)
Not sure what I'm doing wrong.
True or False?
If I put the LHS into my calculator it comes out with the RHS, but I can't do it by hand.
When I do it by hand I get:
1 / (x^2 + x)
Not sure what I'm doing wrong.
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To make things simple, let us take only the denominator of the first term on left hand side
= 1+1/x^2 = (x^2+1)/x^2
Now putting it in the first term we get first term = 1÷(x^2+1)/x^2
=x^2/(x^2+1)
Now putting the second term the whole expression becomes ={ x^2/(x^2+1)}*1/x= x/(x^2+!)
= 1+1/x^2 = (x^2+1)/x^2
Now putting it in the first term we get first term = 1÷(x^2+1)/x^2
=x^2/(x^2+1)
Now putting the second term the whole expression becomes ={ x^2/(x^2+1)}*1/x= x/(x^2+!)
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LHS = ( 1 / ( 1 + ( 1 / x^2 ) ) ) * (1 / x)
= (1 / [(x² + 1)/x²] * (1/x)
= [x² / (x²+1)] * (1/x)
= x² / x(x²+1)
= x / (x² + 1)
= (1 / [(x² + 1)/x²] * (1/x)
= [x² / (x²+1)] * (1/x)
= x² / x(x²+1)
= x / (x² + 1)