3/(<em>x</em> ² - 1) = 3/((<em>x</em> - 1) (<em>x</em> + 1)) = <em>a</em>/(<em>x</em> - 1) + <em>b</em>/(<em>x</em> + 1)
==> 3 = <em>a</em> (<em>x</em> + 1) + <em>b</em> (<em>x</em> - 1)
==> 3 = (<em>a</em> + <em>b</em>) <em>x</em> + <em>a</em> - <em>b</em>
==> <em>a</em> + <em>b</em> = 3 and <em>a</em> - <em>b</em> = 0
==> <em>a</em> = <em>b</em>
==> <em>a</em> + <em>b</em> = 2<em>a</em> = 3 ==> <em>a</em> = 2/3 and <em>b</em> = 2/3
So you have
3/(<em>x</em> ² - 1) = 2/(3(<em>x</em> - 1)) + 2/(3(<em>x</em> + 1))
Answer: 40k⁶-15k⁴
Step-by-step explanation:

The 10 tons should have 37.9% cement.
Let the 25% mixture be x tons
Then the 68% mixture will be (10 -x) tons.
Using formula for mixtures:
Let p for percentage and w for weight in tons.
p₁w₁ + p₂w₂ = pw
25*x + 68*(10-x) = 37.9*10
25x + 680 - 68x = 379
680 - 43x = 379
680 - 379 = 43x
301 = 43x
43x = 301
x = 301/43
x = 7
Recall that x, was for the 25% mixture, 7 tons.
a) For the 68% mixture, = 10 - x = 10 -7 = 3 tons.
b) For the 25% mixture = x = 7 tons.
Answer:
<h2>
y = ¹/₂x + 6</h2>
Step-by-step explanation:
The product of slopes of perpendicular lines is -1
y = - 2x + 6 ⇒ m₁ = - 2
m₁m₂ = -1
-2m₂ = -1
m₂ = ⁻¹/₋₂ = ¹/₂
The Point-Slope form of equation of a line with slope of "m" and passing through point (x₁, y₁) is: y - y₁ = m(x - x₁)
m = ¹/₂
(-2, 5) ⇒ x₁ = -2, y₁ = 5
So the equation in point-slope form:
y - 5 = ¹/₂(x - (-2))
Therefore:
y - 5 = ¹/₂x + 1
y = ¹/₂x + 1 + 5
<h3>
y = ¹/₂x + 6</h3>