Fractional Equations

Front

What is a fractional equation?

Back

A fractional equation is an equation that contains one or more fractions with variables in the numerator, denominator, or both.

Front

How do you solve a fractional equation?

Back

To solve a fractional equation, you typically find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting equation.

Front

What is the first step in solving the equation \( \frac{1}{3}x + \frac{1}{5} = \frac{1}{5}x - 1 \)?

Back

The first step is to eliminate the fractions by multiplying through by the least common multiple (LCM) of the denominators, which in this case is 15.

Front

What is the least common multiple (LCM) of 3 and 5?

Back

The least common multiple (LCM) of 3 and 5 is 15.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation \( \frac{1}{3}x + \frac{1}{5} = \frac{1}{5}x - 1 \)?

Back

The solution to the equation is \( x = -9 \).

Front

What is the significance of checking your solution in a fractional equation?

Back

Checking your solution is important to ensure that it does not make any denominator zero, which would make the original equation undefined.

Front

What is a common mistake when solving fractional equations?

Back

A common mistake is forgetting to check for extraneous solutions that may arise from multiplying both sides by a variable expression.

Front

How can you verify if your solution to a fractional equation is correct?

Back

You can verify your solution by substituting it back into the original equation to see if both sides are equal.

Front

What is the result of \( \frac{1}{3}x + \frac{1}{5} \) when \( x = -9 \)?

Back

When \( x = -9 \), \( \frac{1}{3}(-9) + \frac{1}{5} = -3 + 0.2 = -2.8 \).