Lowest Common Denominator with Rational Expressions

Simplify: \frac{4}{x-1}+\frac{3}{x^2-1}
Which steps are incorrect?

• Factor the denominators to find a LCD

• Factor the numerators to find the LCD

• Multiply the first fraction by the part of the LCD that is missing: x + 1

• Add the numerators

• Combine like terms

Simplify: \frac{5}{6x}-\frac{\left(2x-5\right)}{3x^2}

• Find the LCD

• Multiply the second fraction by the part of the LCD that is missing: 2

• Multiply the first fraction by the part of the LCD that is missing: x

• Combine like terms

• Use the distributive property to eliminate the parenthesis.

Find the lowest common denominators for the fractions:

• There is no common denominator possible.

What error did the student make

• Multiplied the left denominator by the wrong factor

• Multiplied the right denominator by the wrong factor

• Student didn't multiply the numerators by the correct terms

• No error was made by the studnet

Which step contains the first error. There may be more than one correct answer

• Student multiplied both the left and right fraction by the wrong terms

• Student didn't multiply the numerator and denominator

• The student multiplied the numerators incorrectly

• No Error was made by the student

What error did the student make?

• Student multiplied the left expression by the wrong factor

• Student multiplied the right expression by the wrong factor

• The student distributed incorrectly

• The student didn't change their signs to subtract

• No error was made

What is the first step when adding fractions?

• Add right away

• Flip the numerator and denominator

• Find the least common denominator (LCD)

• Find the greatest common factor (GCF)