Oh honey, let's break it down for you. First, you distribute the 2 to both terms inside the parentheses, giving you 2x + 2. Then you combine like terms by adding the 3x to the 2x, which gives you 5x. Finally, add the constant terms together to get your final answer of 5x + 2. Math can be sassy too, you know!
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
"2 over 3x equals 4" is an equation in a single variable, x.2/(3x) = 4 => 3x/2 = 1/4 => 3x = 2/4 = 1/2 => x = 1/6.
3x2 - 7x = -2 3x2 - 7x + 2 = 0 3x2 - 6x - x + 2 = 0 3x(x - 2) - 1(x - 2) = 0 (x - 2)(3x - 1) = 0 so x - 2 = 0 or 3x - 1 = 0 so x = 2 or x = 1/3
3x2 + 5x + 2 is a quadratic expression that can be factored as follows: 3x2 + 5x + 2 = 3x2 + 3x + 2x + 2 = 3x(x + 1) + 2(x + 1) = (3x + 2)(x + 1)
3x - 3x -1 + 2x -1 = 0 0 - 1 + 2x - 1 = 0 2x - 2 = 0 2x = 2 x = 1
x2/(3x2 - 5x - 2) - [2x/ (3x + 1)][1/(x - 2)] = x2/(3x2 - 6x + x - 2) - 2x/(3x + 1)(x - 2) = x2/[3x(x - 2) + (x - 2)] - 2x/(3x + 1)(x - 2) = x2/(3x + 1)(x - 2) - 2x/(3x + 1)(x - 2) = (x2 - 2x)/(3x + 1)(x - 2) = x(x - 2)/(3x + 1)(x - 2) = x/(3x + 1)
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
4
"2 over 3x equals 4" is an equation in a single variable, x.2/(3x) = 4 => 3x/2 = 1/4 => 3x = 2/4 = 1/2 => x = 1/6.
(x + 2)(3x - 1)(3x + 1)
1
3x2 - 7x = -2 3x2 - 7x + 2 = 0 3x2 - 6x - x + 2 = 0 3x(x - 2) - 1(x - 2) = 0 (x - 2)(3x - 1) = 0 so x - 2 = 0 or 3x - 1 = 0 so x = 2 or x = 1/3
(-3x+1)(x+2) = 0 x = -2 or x = 1/3
3x2 + 5x + 2 is a quadratic expression that can be factored as follows: 3x2 + 5x + 2 = 3x2 + 3x + 2x + 2 = 3x(x + 1) + 2(x + 1) = (3x + 2)(x + 1)
3x - 3x -1 + 2x -1 = 0 0 - 1 + 2x - 1 = 0 2x - 2 = 0 2x = 2 x = 1
3x - x = x(3 - 1) = x(2) = 2x
(x+2)(x+1) = x^2 + 1x + 2x + 2 = x^2 + 3x +2