Simplify the expression on its real domain.

01 / Standard#Your turn

\frac{m^{3/2}-m^{-1/2}}{m^{1/2}+m^{-1/2}}

Official paper · jm01-2025 · I.4 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Negative half-powers require m>0.

Hint 2

Multiply numerator and denominator by √m.

Worked solution

Clear fractional powers.
$\frac{m^{3/2}-m^{-1/2}}{m^{1/2}+m^{-1/2}}=\frac{m^2-1}{m+1}$
Factor the difference of squares; m+1 is nonzero on the domain.
$\frac{(m-1)(m+1)}{m+1}=m-1,\quad m>0$

C: m−1, with m>0.

Checks and common pitfalls: Simplification does not enlarge the original domain.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Clear fractional powers.
$\frac{m^{3/2}-m^{-1/2}}{m^{1/2}+m^{-1/2}}=\frac{m^2-1}{m+1}$
Factor the difference of squares; m+1 is nonzero on the domain.
$\frac{(m-1)(m+1)}{m+1}=m-1,\quad m>0$

Think first. Reveal a hint when the class is ready.

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