We can start by simplifying each fraction individually:
1. Simplifying (6x² - 600) / (3x - 30):
Factor out a common factor of 6:
6(x² - 100) / 3(x - 10)
Now simplify the expression further by canceling out common factors:
2(x² - 100) / (x - 10)
2. Simplifying (x² - 100) / (x² (x+10)²):
This fraction can be simplified by factoring the numerator as the difference of squares:
(x - 10)(x + 10) / x²(x + 10)²
Now you can cancel out the common factor of x + 10:
(x - 10) / x²(x + 10)
Now, we can multiply the simplified fractions:
(2(x² - 100) / (x - 10)) * ((x - 10) / x²(x + 10))
= (2(x² - 100) * (x - 10)) / (x - 10)(x²)(x + 10)
= 2x²(x - 10) - 200) / x³(x - 10)(x + 10)
= (2x³ - 20x² - 200) / (x³(x - 10)(x + 10))
Therefore, the fully simplified expression as a single fraction is:
(2x³ - 20x² - 200) / (x³(x - 10)(x + 10))
Fully simplify the expression below and write your answer as a single fraction.
6x^2 -600 over 3x -30 multiply by x^2 -100 over x^2 (x+10)^2
5 answers
wrong
Let's simplify the expression again:
Given expression: (6x^2 - 600) / (3x - 30) * (x^2 - 100) / x^2(x+10)^2
Factor the numerator of the first fraction:
6(x^2 - 100) / 3(x - 10)
Simplify the above expression:
2(x^2 - 100) / (x - 10)
Factor the numerator of the second fraction:
(x - 10)(x + 10) / x^2(x+10)^2
Cancel the common terms:
(x - 10) / x^2(x + 10)
Now, multiply the two fractions together:
[2(x^2 - 100) / (x - 10)] * [(x - 10) / x^2(x + 10)]
This simplifies to:
2(x^2 - 100) / (x^2(x + 10))
Further simplification:
2x^2 - 200 / x^2(x + 10)
Therefore, the fully simplified expression as a single fraction is:
(2x^2 - 200) / (x^2(x + 10))
Given expression: (6x^2 - 600) / (3x - 30) * (x^2 - 100) / x^2(x+10)^2
Factor the numerator of the first fraction:
6(x^2 - 100) / 3(x - 10)
Simplify the above expression:
2(x^2 - 100) / (x - 10)
Factor the numerator of the second fraction:
(x - 10)(x + 10) / x^2(x+10)^2
Cancel the common terms:
(x - 10) / x^2(x + 10)
Now, multiply the two fractions together:
[2(x^2 - 100) / (x - 10)] * [(x - 10) / x^2(x + 10)]
This simplifies to:
2(x^2 - 100) / (x^2(x + 10))
Further simplification:
2x^2 - 200 / x^2(x + 10)
Therefore, the fully simplified expression as a single fraction is:
(2x^2 - 200) / (x^2(x + 10))
make sure to cancel all terms if possible
Apologies for the oversight. Let's simplify the expression again, making sure to cancel all possible terms:
Given expression: (6x^2 - 600) / (3x - 30) * (x^2 - 100) / x^2(x+10)^2
Factor the numerator of the first fraction:
6(x^2 - 100) / 3(x - 10)
Simplify the above expression:
2(x + 10)(x - 10) / (x - 10)
Simplify further:
2(x + 10)
Factor the numerator of the second fraction:
(x - 10)(x + 10) / x^2(x+10)^2
Cancel the common terms:
(x - 10) / x^2(x + 10)
Now, multiply the two simplified fractions:
[2(x + 10)] * [(x - 10) / x^2(x + 10)]
This simplifies to:
2(x + 10)(x - 10) / x^2(x + 10)
Further simplification:
2(x^2 - 100) / x^2(x + 10)
By expanding and simplifying the numerator:
2x^2 - 200 / x^2(x + 10)
Therefore, the fully simplified expression as a single fraction is:
(2x^2 - 200) / (x^2(x + 10))
Given expression: (6x^2 - 600) / (3x - 30) * (x^2 - 100) / x^2(x+10)^2
Factor the numerator of the first fraction:
6(x^2 - 100) / 3(x - 10)
Simplify the above expression:
2(x + 10)(x - 10) / (x - 10)
Simplify further:
2(x + 10)
Factor the numerator of the second fraction:
(x - 10)(x + 10) / x^2(x+10)^2
Cancel the common terms:
(x - 10) / x^2(x + 10)
Now, multiply the two simplified fractions:
[2(x + 10)] * [(x - 10) / x^2(x + 10)]
This simplifies to:
2(x + 10)(x - 10) / x^2(x + 10)
Further simplification:
2(x^2 - 100) / x^2(x + 10)
By expanding and simplifying the numerator:
2x^2 - 200 / x^2(x + 10)
Therefore, the fully simplified expression as a single fraction is:
(2x^2 - 200) / (x^2(x + 10))