Foundations

Equivalent Expressions on the SAT: Desmos Walkthrough

Use Desmos to test whether two expressions are equal for every

x

by graphing both as

y=

and checking if the curves land perfectly on top of each other, or by graphing their difference and looking for the flat line

y=0

This is a Foundations lesson: the core Desmos moves (graphing both sides, plotting points, reading intersections) that every other technique in the course builds on.

Take this lesson interactively

A real SAT-style question

Which expression is equivalent to $\frac{4}{4 x - 5} - \frac{1}{x + 1}$ ?

$\frac{1}{(x + 1) (4 x - 5)}$

$\frac{3}{3 x - 6}$

$- \frac{1}{(x + 1) (4 x - 5)}$

$\frac{9}{(x + 1) (4 x - 5)}$

How to solve it in Desmos, step by step

The idea

Graph the original expression, then graph choice D on top of it. If the two curves land exactly on each other, the expressions are equivalent.

1
Step 1
Type the original expression as a function. Desmos draws its curve.
Type in Desmos
$y=\frac{4}{4x-5}-\frac{1}{x+1}$
2
Step 2
On the next line, type choice D as a second function. Watch its curve land exactly on top of the first one.
Type in Desmos
$y=\frac{9}{(x+1)(4x-5)}$
3
Step 3
Click the colored circle next to the first equation to hide it, then click it again to show it. Since choice D traces the same curve and never separates from the original, the answer is D.

The answer is D.

$\frac{9}{(x + 1) (4 x - 5)}$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

Which expression is equivalent to

\dfrac{3}{3x-2} - \dfrac{1}{x+4}

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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