![\bf \begin{cases} f(x)=2x-1\\ g(x)=x^2+3x-1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)+g(x)\implies (2x-1)+(x^2+3x-1)\implies 2x+3x-1-1+x^2 \\\\\\ x^2+5x-2 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Af%28x%29%3D2x-1%5C%5C%0Ag%28x%29%3Dx%5E2%2B3x-1%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Af%28x%29%2Bg%28x%29%5Cimplies%20%282x-1%29%2B%28x%5E2%2B3x-1%29%5Cimplies%202x%2B3x-1-1%2Bx%5E2%0A%5C%5C%5C%5C%5C%5C%0Ax%5E2%2B5x-2%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill)
![\bf f(x)-g(x)\implies (2x-1)-(x^2+3x-1)\implies 2x-1-x^2-3x+1 \\\\\\ -x^2-x \\\\[-0.35em] ~\dotfill\\\\ f(x)\cdot g(x)\implies (2x-1)\cdot (x^2+3x-1) \\\\\\ \stackrel{2x(x^2+3x-1)}{2x^3+6x^2-2x}~~+~~\stackrel{-1(x^2+3x-1)}{(-x^2-3x+1)}\implies 2x^3+5x^2-5x+1 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{f(x)}{g(x)}\implies \cfrac{2x-1}{x^2+3x-1}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29-g%28x%29%5Cimplies%20%282x-1%29-%28x%5E2%2B3x-1%29%5Cimplies%202x-1-x%5E2-3x%2B1%0A%5C%5C%5C%5C%5C%5C%0A-x%5E2-x%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0Af%28x%29%5Ccdot%20g%28x%29%5Cimplies%20%282x-1%29%5Ccdot%20%28x%5E2%2B3x-1%29%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7B2x%28x%5E2%2B3x-1%29%7D%7B2x%5E3%2B6x%5E2-2x%7D~~%2B~~%5Cstackrel%7B-1%28x%5E2%2B3x-1%29%7D%7B%28-x%5E2-3x%2B1%29%7D%5Cimplies%202x%5E3%2B5x%5E2-5x%2B1%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0A%5Ccfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%5Cimplies%20%5Ccfrac%7B2x-1%7D%7Bx%5E2%2B3x-1%7D)
the division doesn't simplify any further.
Answer:
C. 1 / (a(a - 1))
Step-by-step explanation:
View Image
Just know that:
n! = n(n-1)!
= n(n-1)(n-2)!
= n(n-1)(n-2)(n-3)!
= ...
Answer:
The equation of the line is 6y = 7x + 23
Step-by-step explanation:
We begin by calculating the slope of the line;
mathematically, the slope is given by;
m = (y2-y1)/(x2-x1)
That would be;
m= (5-(-2))/(1-(-5))
m = 7/6
So the equation becomes;
y = 7/6x + b
We below need to get the value of the y-intercept b
We get this by making a substitution for any of the two points
Let’s say we make the substitution for (-5,-2) in which case y = -2 and x = -5
Thus, we have
-2 = 7/6(-5) + b
-2 = -35/6 + b
b = -2 + 35/6
b = (-12+ 35)/6 = 23/6
So we have;
y = 7/6x + 23/6
let’s multiply through by 6
6y = 7x + 23
