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))
The equation would be 2n-7
About 2.4 pounds away from 12.9 pounds.
small or less than
Answer:
AB + BC = AC
BC = AC - AB
5x + 6 = 37 - (2 x + 3) = 37 -2 x - 3 = 34 - 2 x
7 x = 34 - 6 = 28
x = 4
BC = 5 x + 6 = 5 * 4 + 6 = 26
Check:
AB = 2 x + 3 = 2 * 4 + 3 = 11
AB + BC = 26 + 11 = 37
Answer:
y = x + 2
Step-by-step explanation:
Each y variable is set to be two more than the x variable. This makes the the slope intercept form y = x + 2.
