Math / Algebra

Question $\frac{a^{y}b - ab^{y}}{a^{r} - ab}$

Studdy Solution

STEP 1

1. The expression involves factoring and simplifying.
2. $a$ and $b$ are non-zero to avoid division by zero.

STEP 2

1. Factor the numerator.
2. Factor the denominator.
3. Simplify the expression by canceling common factors.

STEP 3

Factor the numerator $a^{y}b - ab^{y}$ .
\[ a^{y}b - ab^{y} = ab(a^{y-1} - b^{y-1}) $

STEP 4

Factor the denominator $a^{r} - ab$ .
\[ a^{r} - ab = a(a^{r-1} - b) $

STEP 5

Simplify the expression by canceling common factors.
\[ \frac{ab(a^{y-1} - b^{y-1})}{a(a^{r-1} - b)} = \frac{b(a^{y-1} - b^{y-1})}{a^{r-1} - b} $
Note: Further simplification depends on specific values or relationships between $y$ , $r$ , and other variables.

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Question $\frac{a^{y}b - ab^{y}}{a^{r} - ab}$

Studdy Solution

STEP 1

1. The expression involves factoring and simplifying.
2. $a$ and $b$ are non-zero to avoid division by zero.

STEP 2

1. Factor the numerator.
2. Factor the denominator.
3. Simplify the expression by canceling common factors.

STEP 3

Factor the numerator $a^{y}b - ab^{y}$ .
\[ a^{y}b - ab^{y} = ab(a^{y-1} - b^{y-1}) $

STEP 4

Factor the denominator $a^{r} - ab$ .
\[ a^{r} - ab = a(a^{r-1} - b) $

STEP 5

Simplify the expression by canceling common factors.
\[ \frac{ab(a^{y-1} - b^{y-1})}{a(a^{r-1} - b)} = \frac{b(a^{y-1} - b^{y-1})}{a^{r-1} - b} $
Note: Further simplification depends on specific values or relationships between $y$ , $r$ , and other variables.

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Questionayb−abyar−ab\frac{a^{y}b - ab^{y}}{a^{r} - ab}ar−abayb−aby​

Studdy Solution

STEP 1

1. The expression involves factoring and simplifying.2. a a a and b b b are non-zero to avoid division by zero.

STEP 2

1. Factor the numerator.2. Factor the denominator.3. Simplify the expression by canceling common factors.

STEP 3

Factor the numerator ayb−aby a^{y}b - ab^{y} ayb−aby.\[ a^{y}b - ab^{y} = ab(a^{y-1} - b^{y-1}) $

STEP 4

Factor the denominator ar−ab a^{r} - ab ar−ab.\[ a^{r} - ab = a(a^{r-1} - b) $

STEP 5

Simplify the expression by canceling common factors.\[ \frac{ab(a^{y-1} - b^{y-1})}{a(a^{r-1} - b)} = \frac{b(a^{y-1} - b^{y-1})}{a^{r-1} - b} $Note: Further simplification depends on specific values or relationships between y y y, r r r, and other variables.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\frac{a^{y}b - ab^{y}}{a^{r} - ab}$

1. The expression involves factoring and simplifying.
2. $a$ and $b$ are non-zero to avoid division by zero.

1. Factor the numerator.
2. Factor the denominator.
3. Simplify the expression by canceling common factors.

Factor the numerator $a^{y}b - ab^{y}$ .
\[ a^{y}b - ab^{y} = ab(a^{y-1} - b^{y-1}) $

Factor the denominator $a^{r} - ab$ .
\[ a^{r} - ab = a(a^{r-1} - b) $

Simplify the expression by canceling common factors.
\[ \frac{ab(a^{y-1} - b^{y-1})}{a(a^{r-1} - b)} = \frac{b(a^{y-1} - b^{y-1})}{a^{r-1} - b} $
Note: Further simplification depends on specific values or relationships between $y$ , $r$ , and other variables.