Question

simplify (1/x) + (1/ (x+h)

Answer 1

1) (1/x)/h --> 1/x/h/1 multiply denominator reciprocal to both sides, cancelling out the bottom [1/xh]

(1/x+h)+(1/xh)

2) multiply 1st h by x/x: h--> hx/x and add to 1/x. [(1+hx)/x]

(1+hx)/x+1/xh

3) multiply 1st term by h/h. (1+hx)/x --> (h+xh^2)/xh

(h+xh^2)/xh+1/xh

4) Now just combine. (h+xh^2)/xh+1/xh --> (xh^2+h+1)/xh