Using the '/' sign as 'over',

Using ' ^ ' sign to signal a power such as x^2 is x squared.

To simplify, multiply (1 / x + h) by (x / x) which is a value of one. Then multiply 1/x by (x+h) / (x+h), another value of one. By doing so, you create common denominators.

(1 / x + h) * (x / x) =

x / (x^2 + hx)

And

(1 / x) * [(x + h) / (x + h)] =

(x + h) / (x^2 +hx)

Notice in the second line of each equation, the denominator of x^2 + hx is the same. This allows us to combine the two fractions by subtracting the numerators while keeping the same denominator.

X - (x+h) / (x^2 + hx)

Then distribute the negative sign in the numerator

x - x - h / (x^2 + hx)

The two xs cancel out leaving:

-h / (x^2 + hx) which is your answer.

Using ' ^ ' sign to signal a power such as x^2 is x squared.

To simplify, multiply (1 / x + h) by (x / x) which is a value of one. Then multiply 1/x by (x+h) / (x+h), another value of one. By doing so, you create common denominators.

(1 / x + h) * (x / x) =

x / (x^2 + hx)

And

(1 / x) * [(x + h) / (x + h)] =

(x + h) / (x^2 +hx)

Notice in the second line of each equation, the denominator of x^2 + hx is the same. This allows us to combine the two fractions by subtracting the numerators while keeping the same denominator.

X - (x+h) / (x^2 + hx)

Then distribute the negative sign in the numerator

x - x - h / (x^2 + hx)

The two xs cancel out leaving:

-h / (x^2 + hx) which is your answer.