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.