write in lowest term (2x+7)(x-1)/(2x+3)(2x+7)
I will assume you meant to write
(2x+7)(x-1)/((2x+3)(2x+7))
then ..
(2x+7)(x-1)/((2x+3)(2x+7))
= (x-1)/(2x+3), where x is not equal to -7/2
(x-1)/(2x+3) is the answer because the (2x+7) in the numerator and denominator cancels out.
right (x-1)/(2x+3) is the answer
To simplify the expression (2x+7)(x-1)/(2x+3)(2x+7) and write it in lowest terms, we can simplify both the numerator and the denominator and then cancel out any common factors.
Let's start by simplifying the numerator: (2x+7)(x-1)
To multiply binomials, you can use the FOIL method, which stands for First, Outer, Inner, Last:
First: 2x * x = 2x^2
Outer: 2x * -1 = -2x
Inner: 7 * x = 7x
Last: 7 * -1 = -7
Now let's combine these terms: 2x^2 - 2x + 7x - 7
Simplifying further: 2x^2 + 5x - 7
Next, let's simplify the denominator: (2x+3)(2x+7)
Again, we can use the FOIL method:
First: 2x * 2x = 4x^2
Outer: 2x * 7 = 14x
Inner: 3 * 2x = 6x
Last: 3 * 7 = 21
Combining these terms: 4x^2 + 14x + 6x + 21
Simplifying further: 4x^2 + 20x + 21
Now we can rewrite the expression as:
(2x^2 + 5x - 7) / (4x^2 + 20x + 21)
To find the lowest terms, we need to check if there are any common factors that can be canceled out in both the numerator and denominator.
In this case, it seems that there are no common factors that can be canceled out. Therefore, the simplified expression, written in lowest terms, remains:
(2x^2 + 5x - 7) / (4x^2 + 20x + 21)