#48
Top 50 Mistake
Not multiplying all terms when finding common denominator
"The Missing Multiply"
The Mistake in Action
Simplify $\frac{3}{x} + \frac{2}{x+1}$
Wrong: $= \frac{3(x+1)}{x(x+1)} + \frac{2}{x(x+1)}$ $= \frac{3x + 3 + 2}{x(x+1)} = \frac{3x + 5}{x(x+1)}$
Why It Happens
When finding a common denominator, students multiply the numerator of one fraction but forget to multiply the other.
The Fix
Both fractions need their numerators multiplied by the appropriate factor.
$\frac{3}{x} + \frac{2}{x+1}$
Common denominator: $x(x+1)$
$= \frac{3(x+1)}{x(x+1)} + \frac{2 \times x}{x(x+1)}$
$= \frac{3x + 3 + 2x}{x(x+1)} = \frac{5x + 3}{x(x+1)}$
Spot the Mistake
Can you identify where this student went wrong?
$\frac{3(x+1)}{x(x+1)}$
$+ \frac{2}{x(x+1)}$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: