How would you set this up? Express the following in its simplest form.

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1 Answer
Jan 28, 2018

x-1x1

Explanation:

"to eliminate fractions multiply numerator/denominator "to eliminate fractions multiply numerator/denominator
"by x"by x

rArr(x-1/x)/(1+1/x)xx x/xx1x1+1x×xx

=(x^2-1)/(x+1)=x21x+1

"factorise numerator and cancel common factors"factorise numerator and cancel common factors

x^2-1" is a "color(blue)"difference of squares"x21 is a difference of squares

rArrx^2-1=(x-1)(x+1)x21=(x1)(x+1)

rArr(x^2-1)/(x+1)x21x+1

=((x-1)cancel((x+1)))/cancel((x+1))

=x-1larr" in the form "Ax+B

"with "A=1" and "B=-1