Solving Rational Equations

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Step 1: Find the LCD

To solve, we first need to clear the fractions. Tap the factors below to build the Least Common Denominator (LCD).

Your LCD: Select factors above

Step 2: Clear the Fractions

Drag the LCD block below into each of the 3 drop zones to multiply both sides and clear the fractions.

+
=
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auto_awesome Great job! The fractions are cleared.

Step 3: Check for Extraneous Solutions

We solved and got .

Slide the point to on the number line to plug it into the denominator.

Denominator:
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Oh no! The denominator is zero.
Division by zero is undefined.
What do we call this type of solution?

Not quite! If it makes the denominator zero, we must reject it.

check_circle Correct! Extraneous solutions must be rejected.

Step 4: Real-World Application

Pipe A can fill a pool in {{state.s4_A}} hours.
Pipe B can fill it in {{state.s4_B}} hours.

Build the correct rational equation to find how long () it takes them working together.

Tap the boxes to cycle options

Pipe A
Rate
Pipe B
Rate
Together
Rate
task_alt Perfect! You built the equation.
🏆

Challenge Complete!

You've mastered clearing fractions, rejecting extraneous solutions, and building rational equations!

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