We read your photo as:

Simplify the expression 2 - (y3)/(x4)(y4-y3)/(x4)

Mathematics

ScanSolve AI Answer

Answer

2y−3y−1\frac{2y-3}{y-1}

Step-by-step solution

3 steps
  1. Simplify the complex fraction inside the parenthesis.

    The complex fraction is y3x4y4−y3x4\frac{\frac{y^3}{x^4}}{\frac{y^4-y^3}{x^4}}.
    To simplify, multiply the numerator by the reciprocal of the denominator:

    y3x4⋅x4y4−y3\frac{y^3}{x^4} \cdot \frac{x^4}{y^4-y^3}

    Cancel out the x4x^4 terms:

    =y3y4−y3= \frac{y^3}{y^4-y^3}

    Factor out y3y^3 from the denominator:

    =y3y3(y−1)= \frac{y^3}{y^3(y-1)}

    Cancel out y3y^3 (assuming y≠0y \neq 0):

    =1y−1= \frac{1}{y-1}
  2. Substitute the simplified complex fraction back into the original expression.

    The expression becomes:

    2−1y−12 - \frac{1}{y-1}
  3. Combine the terms into a single fraction.

    To do this, find a common denominator, which is (y−1)(y-1):

    =2(y−1)y−1−1y−1= \frac{2(y-1)}{y-1} - \frac{1}{y-1}

    Combine the numerators:

    =2(y−1)−1y−1= \frac{2(y-1) - 1}{y-1}

    Distribute the 2 in the numerator and simplify:

    =2y−2−1y−1= \frac{2y - 2 - 1}{y-1} =2y−3y−1= \frac{2y - 3}{y-1}

    The simplified expression is 2y−3y−1\frac{2y-3}{y-1}.

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
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