Simplify
7x^2+45x+18/(x^3+12x^2+36x)
Please help.
Thank you.
7x^2+45x+18 = (7x+3)(x+6)
x^3+12x^2+36x = x(x+6)^2
so, dividing, you are left with
(7x+3)/(x(x+6))
(7x+3)/x(x+6)^2 can be simplified to
(7x+3)/(x^2+6x)^2 which can be simplified to...
(7x+3)/(x^4)+(6x^2)
what is the area of 32cm
To simplify the given expression, we can start by factoring both the numerator and the denominator.
Let's start with the numerator: 7x^2 + 45x + 18.
To find the factors of this quadratic expression, we need to look for two numbers that multiply to give 7 * 18 = 126 and add up to 45. The numbers that meet these criteria are 3 and 42.
So, we can rewrite the numerator as: 7x^2 + 3x + 42x + 18.
Now, we can group the terms and factor by grouping:
(7x^2 + 3x) + (42x + 18).
Taking out the common factors from each group, we get:
x(7x + 3) + 6(7x + 3).
Now, we can notice that we have a common binomial factor of (7x + 3). So, we can factor that out:
(7x + 3)(x + 6).
Moving on to the denominator: x^3 + 12x^2 + 36x.
We can factor out x from each term:
x(x^2 + 12x + 36).
Now, let's factor the quadratic expression within the parentheses. The factors of 36 that add up to 12 are 6 and 6.
So, we can rewrite the denominator as: x(x + 6)(x + 6).
Now that we have factored both the numerator and the denominator, we can simplify the expression:
(7x + 3)(x + 6) / (x)(x + 6)(x + 6).
Simplifying further, we can cancel out the common factors:
(7x + 3) / (x)(x + 6).
And that's the simplified form of the expression.