simplify 7/(25z^3y)-1/(35z^2y) — step-by-step solution

Let's sum the fractions:

\frac{7}{25 z^{3} y} - \frac{1}{35 z^{2} y}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{7}{25 z^{3} y} - \frac{1}{35 z^{2} y}

\frac{7 \cdot 35 z^{2} y - 1 \cdot 25 z^{3} y}{25 z^{3} y \cdot 35 z^{2} y}

\frac{7 \cdot 35 z^{2} y - 1 \cdot 25 z^{3} y}{25 z^{3} y \cdot 35 z^{2} y}

ⓘ Multiplications are done before additions and subtractions:

7 \cdot 35

7 \cdot (30 + 5)

7 \cdot 30 + 7 \cdot 5

210 + 35

245

1 \cdot 25 z^{3} y

25 z^{3} y

■Multiplying powers with the same base adds the exponents:

z^{3} \cdot y \cdot z^{2} \cdot y

z^{5} y^{2}

ⅰ

25 \cdot 35

(20 + 5) \cdot 35

20 \cdot 35 + 5 \cdot 35

700 + 175

875

\frac{245 z^{2} y - 25 z^{3} y}{875 z^{5} y^{2}}

ⓘ A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{245 z^{2} y - 25 z^{3} y}{875 z^{5} y^{2}}

\frac{49 z^{2} y - 5 z^{3} y}{175 z^{5} y^{2}}

\frac{49 z^{2} y - 5 z^{3} y}{175 z^{5} y^{2}}

ⓘ What the terms have in common is factored out, so that the fraction can be simplified:

\frac{49 z^{2} y - 5 z^{3} y}{175 z^{5} y^{2}}

\frac{y z^{2} \cdot (49 - 5 z)}{175 z^{5} y^{2}}

\frac{y z^{2} \cdot (49 - 5 z)}{175 z^{5} y^{2}}

We simplify the fraction:

\frac{y}{y^{2}}

by the common factor:

y

to get the new quotient:

\frac{1}{y}

We simplify the fraction:

\frac{z^{2}}{z^{5}}

by the common factor:

z^{2}

to get the new quotient:

\frac{1}{z^{3}}

\frac{49 - 5 z}{175 \cdot z^{3} y}

▶Result:

\frac{49 - 5 z}{175 y z^{3}}