We read your photo as:

Find the least common denominator (LCD) for the two fractions.

Mathematics

ScanSolve AI Answer

Answer

−u3−2u2v+uv−v3uv2\frac{-u^3 - 2u^2v + uv - v^3}{uv^2}

Step-by-step solution

5 steps

  1. Find the least common denominator (LCD) for the two fractions.

    The denominators are uvuv and v2v^2. The LCD of uvuv and v2v^2 is uv2uv^2.

  2. Rewrite each fraction with the LCD.

    For the first fraction, multiply the numerator and denominator by vv:

    u2−v2uv=(u2−v2)⋅vuv⋅v=u2v−v3uv2\frac{u^2 - v^2}{uv} = \frac{(u^2 - v^2) \cdot v}{uv \cdot v} = \frac{u^2v - v^3}{uv^2}

    For the second fraction, multiply the numerator and denominator by uu:

    v−3uv−u2v2=(v−3uv−u2)⋅uv2⋅u=uv−3u2v−u3uv2\frac{v - 3uv - u^2}{v^2} = \frac{(v - 3uv - u^2) \cdot u}{v^2 \cdot u} = \frac{uv - 3u^2v - u^3}{uv^2}

  3. Add the rewritten fractions.

    u2v−v3uv2+uv−3u2v−u3uv2=u2v−v3+uv−3u2v−u3uv2\frac{u^2v - v^3}{uv^2} + \frac{uv - 3u^2v - u^3}{uv^2} = \frac{u^2v - v^3 + uv - 3u^2v - u^3}{uv^2}

  4. Combine like terms in the numerator.

    Combine the terms involving u2vu^2v: u2v−3u2v=−2u2vu^2v - 3u^2v = -2u^2v.
    Rearrange the terms in the numerator:

    −u3−2u2v+uv−v3-u^3 - 2u^2v + uv - v^3

  5. Write the simplified expression.

    −u3−2u2v+uv−v3uv2\frac{-u^3 - 2u^2v + uv - v^3}{uv^2}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QFind a common denominator for the two fractions.QFind a common denominator for all fractions.QCalculate the LCM of two numbers and add/subtract fractions.QMultiply all terms by the least common multiple (LCM) of the denominators (4 and 5), which is 20, to…QCombine the fractions using a common denominator.
Browse by topic:Pre-Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp