How Do You Use the Difference Quotient with Fractions?

A difference quotient is said to be an expression that represents the difference between two function values, which is divided by the difference between two points. Usually, it is used to calculate the slope of a secant line between two points on the graph for the function. Just for the review, a function is called a line or a curve that has only one y value for every x value. The difference quotient is called a measurement of the average rate of change of the function with respect to an interval. There are times when the calculations become difficult because of the complex figures. For ease, you can use an online difference quotient calculator that calculates the difference quotient for the given function within no time.

Difference quotient:

The difference quotient is known as a measure of the average rate of change of function f(x) with respect to “x” at an interval. While the given function is said to be the difference that describes the slope of the line passing through the points of the curve. Click this post to more about bill of sale for your business which will be helpful in your business. The calculations for the difference quotient can be done by using the formula, but instead of using the formula, you can consider the difference of quotient solver through which you can easily determine the slope of a curved line in between two different points.

Difference Quotient Formula:

The difference quotient formula is used to determine the difference quotient and the formula looks like this:

f x+h-f (x)h

You can use the online Difference Quotient Calculator that displays the difference quotient for the given function along with the step-by-step procedure. For calculating it manually you need to follow the below steps

  • Insert x + h into the function f and evaluate to find f (x + h).
  • Now, you have f (x + h) so, find f (x + h) by inserting the values of f (x + h) & f(x)
  • Put the result form the step 2 for the numerator and simplify the calculations.

When the limit is taken into account, then the limit h approaches zero gives the derivative of the function f. However, the calculation is still difficult for people who are not good at doing calculations. Simply, they can try the Difference Quotient Calculator to find the derivative of quotients, which is the difference quotient between two points of the curve.

Using of Difference Quotient with Fractions:

You will need to calculate the difference quotient in the same way as you do for any other kind of non-fraction function. The thing that makes the calculations complicated is that when you end up with the little fractions inside of the “big fraction”. The trick to getting rid of those little fractions is to multiply the numerator & denominator of the big fraction by the common denominator of the little fractions. In this way, you will get the fractions to cancel out in a simple and quick step.

Then you can easily multiply & simplify the numerator, and then cancel out “h” from the numerator & denominator. This process will work every time whenever you find the difference quotient for a fraction. Determining the difference quotient can be confusing when your function is a fraction, but using the above-mentioned method is an easy way to handle it. You can also use the difference quotient calculator to find the difference quotient of a given function within a fraction of seconds.


By reading this post, we came to know what exactly the difference quotient is and how to solve the difference quotient with fractions. The standard formula for the difference quotient is also taken into account. If you still face issues at the time of calculating, then you can consider the “find the difference quotient calculator” that shows the stepwise calculations for the function.

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