Back to Perform rational expression operations — Problem 2 · Task Set 22

Exercises: Rational Expression Arithmetic (Add, Subtract, Multiply, Divide)

This is an advanced (+) topic. Work through each section in order. Factor all numerators and denominators before multiplying or dividing. State domain restrictions for all problems.

Grade 10·19 problems·~45 min·Common Core Math - HS Algebra·standard·hsa-apr-d-7

Work through problems with immediate feedback

Fluency Practice

$Two-column card showing the wrong approach (canceling x terms from a sum) versus the correct approach (only whole factors that multiply the entire numerator and denominator can cancel).$

A student simplifies $\dfrac{x + 3}{x + 5}$ and claims the $x$ cancels to give $\dfrac{3}{5}$ . Which statement correctly identifies the error?

The $x$ in $x + 3$ and the $x$ in $x + 5$ are terms being added, not factors multiplying the entire numerator and denominator. Only common factors (not terms) can be canceled.

The $x$ can cancel, but only if the student also cancels the constants: $\frac{x+3}{x+5} = \frac{3}{5}$ is correct when $x = 0$ .

The student should have subtracted the $x$ 's instead: $\frac{x+3}{x+5} = \frac{3}{5}$ is wrong; $\frac{0+3}{0+5} = \frac{3}{5}$ is correct.

There is no error — $\frac{x+3}{x+5}$ is always equal to $\frac{3}{5}$ .