What is ((a-x)^3)/(a^3-x^3) ?

The solution to ((a-x)^3)/(a^3-x^3) is ((a-x)^2)/(a^2+xa+x^2)

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simplify ((a-x)^3)/(a^3-x^3)

simplify

\frac{( a - x ) ^{3}}{a ^{3} - x ^{3}}

\frac{( a - x ) ^{2}}{a ^{2} + x a + x ^{2}}

Solution steps

\frac{( a - x ) ^{3}}{a ^{3} - x ^{3}}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

a^{3} - x^{3} = (a - x) (a^{2} + a x + x^{2})

= \frac{( a - x ) ^{3}}{( a - x ) ( a ^{2} + a x + x ^{2} )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(a - x)^{3} = (a - x) (a - x)^{2}

= \frac{( a - x ) ( a - x ) ^{2}}{( a - x ) ( a ^{2} + x a + x ^{2} )}

Cancel the common factor:

a - x

= \frac{( a - x ) ^{2}}{a ^{2} + x a + x ^{2}}

- 2 48 x^{3}

\frac{9}{6} - \frac{4}{5}

- \frac{1}{2}

\frac{( x + y ) ^{2} - x ^{2}}{y}

3 m^{2} - 2 m + 4 m

What is ((a-x)^3)/(a^3-x^3) ?
The solution to ((a-x)^3)/(a^3-x^3) is ((a-x)^2)/(a^2+xa+x^2)