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: 3 mph
Step-by-step explanation:
1. 1/2 mph for 1/2 an hour as they said, meaning that they would've walked for 3 miles kn an hour.
2. 4 and 1/2 miles.
3 + 1 2/4. = 4 1/2
3. 1 3/4 hours.
3 + 2.25 = 5.25
3 x .75 = 2.25
3 miles per hour.
Answer:
189.6
Step-by-step explanation:
790*4=3160*6%
Answer:
x = 4/5
Step-by-step explanation:
Group like terms together. Start by subtracting 1 from both sides, obtaining
5x = -4 + 10x.
Then combine the x terms, obtaining 4 = 5x.
Solving for x by dividing both sides by 5, we get x = 4/5.
