Questions: Упростите выражение (9b)/(a-b) * (a^2-ab)/(54b) и найдите его значение при a=-63, b=9,6. В ответе запишите найденное значение.

Transcript text: Упростите выражение $\frac{9 b}{a-b} \cdot \frac{a^{2}-a b}{54 b}$ и найдите его значение при $a=-63, b=9,6$. В ответе запишите найденное значение.

Solution

Solution Steps

To simplify the expression $\frac{9b}{a-b} \cdot \frac{a^2-ab}{54b}$, we can first simplify the multiplication of the two fractions by canceling out common terms in the numerator and the denominator. After simplification, substitute the given values $a = -63$ and $b = 9.6$ into the simplified expression to find its value.

Step 1: Simplify the Expression

The given expression is $\frac{9b}{a-b} \cdot \frac{a^2-ab}{54b}$. We can simplify this by multiplying the numerators and denominators:

\[ \frac{9b \cdot (a^2 - ab)}{(a-b) \cdot 54b} \]

Cancel out the common term $b$ in the numerator and the denominator:

\[ \frac{9(a^2 - ab)}{54(a-b)} \]

Further simplify by dividing both the numerator and the denominator by 9:

\[ \frac{a^2 - ab}{6(a-b)} \]

Step 2: Substitute the Given Values

Substitute $a = -63$ and $b = 9.6$ into the simplified expression:

\[ \frac{(-63)^2 - (-63) \cdot 9.6}{6(-63 - 9.6)} \]

Calculate the values:

\[ \frac{3969 + 604.8}{6 \times (-72.6)} \]