Simplify each expression. State any excluded values.
(2x^2 + 6x) / 10x^3
cancel 2x top and bottom
2x(x+3) / 2x(5x^2)
(x+3) / 5x^2
Thanks much!!!
To simplify the expression (2x^2 + 6x) / 10x^3, we can separate the numerator and denominator and simplify each part individually.
First, let's simplify the numerator, which is (2x^2 + 6x).
Step 1: Factor out the common factor.
In this case, the common factor is 2x. Factoring it out gives us:
2x(x + 3)
Now, let's simplify the denominator, which is 10x^3.
Step 1: Factor out the common factor.
In this case, the common factor is 10x^3. Factoring it out gives us:
10x^3(1)
Now, combining the simplified numerator and denominator, we get:
(2x(x + 3)) / (10x^3(1))
Simplifying further, we can cancel out the common factors of 2 and 10 in the numerator and denominator, and the x^3 in the denominator:
(x + 3) / (5x^2)
So the simplified expression is (x + 3) / (5x^2).
As for the excluded values, we need to determine any values of x that make the denominator equal to zero, as division by zero is undefined. In this case, the denominator is 5x^2, which would be zero if x equals zero. Therefore, the excluded value is x = 0.