The only factoring you need to do is already done for you:
<em>x</em>² + <em>x</em> - 12 = (<em>x</em> + 4) (<em>x</em> - 3)
What you're asked to do is decompose
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12)
into partial fractions, i.e. find <em>a</em> and <em>b</em> such that
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = <em>a</em> / (<em>x</em> + 4) + <em>b</em> / (<em>x</em> - 3)
Multiply both sides by <em>x</em>² + <em>x</em> - 12 :
3<em>x</em> - 4 = <em>a</em> (<em>x</em> - 3) + <em>b</em> (<em>x</em> + 4)
3<em>x</em> - 4 = (<em>a</em> + <em>b</em>) <em>x</em> + (-3<em>a</em> + 4<em>b</em>)
So we have
<em>a</em> + <em>b</em> = 3
-3<em>a</em> + 4<em>b</em> = -4
and solving this system gives
<em>a</em> = 16/7 and <em>b</em> = 5/7
so you should submit the numbers in bold:
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = 16 / (7 (<em>x</em> + 4)) + 5 / (7 (<em>x</em> - 3))
Answer:
The porch is 17 ft by 17 ft
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
P = 4( 3x+2)
P = 12x+8
We know P = 14x-2
14x-2 = 12x+8
Subtract 12x from each side
14x-2 -12x = 12x+8-12x
2x -2 = 8
Add 2 to each side
2x-2 +2 = 8+2
2x= 10
Divide by 2
2x/2 = 10/2
x = 5
The side is 3x+2
3*5+2
15+2
17
The porch is 17 ft by 17 ft
Answer:
Cost of popcorn= $9.25 - $1.75 ÷ 3
Cost of popcorn= $7.50 ÷ 3
Cost of popcorn= $2.50 per box
Step-by-step explanation:
I am not that sure about the equation, but I know the answer
Answer:
Multiply x + y = 3 by 3 and add it to -3x - 2y = -7
Step-by-step explanation:
When using elimination to solve a system of equations, you multiply one equation by some number. The reason for doing this is that when you add it to the second equation, you want one variable to cancel out. When one variable cancels out (in this case x), you can solve for the other variable (in this case y). I will show this:
3(x + y = 3) = 3x + 3y = 9
3x + 3y = 9
+ -3x + -2y = -7
---------------------------
y = 2
Now, knowing that y = 2, you can substitute y=2 into either equation to solve for x.
-3x - 2(2) = -7
-3x -4 = -7
-3x = -3
x = 1 | to double check (1, 2) as your answer plug these values into both equations
Finding this solution would not have been possible if not for cancelling out the x's above. The other three are wrong because none of the other options cancels out one of the variables.
The simplified expression of 
is 
.
Solution:
Given expression is 
.
To simplify the given expression.
Using exponent rule: 
Using another exponent rule: 
Using exponent rule:
Hence the simplified expression of is .
