Answer:
f(x) = 7/(x+3) -38/(x+3)²
Step-by-step explanation:
The denominator is a perfect square, so the decomposition to fractions will involve both a linear denominator and a quadratic denominator.
You can start with the form ...
... f(x) = B/(x+3) + A/(x+3)²
and write this sum as ...
... f(x) = (Bx +3B +A)/(x+3)²
Equating coefficients gives ...
... Bx = 7x . . . . . B = 7
... 3B +A = -17 . . . . the constant term
... 21 +A = -17 . . . . filling in the value of B
... A = -38 . . . . . . . subtract 21 to find A
Now, we know ...
... f(x) = 7/(x+3) -38/(x+3)²
Well (3-2^2)5 = -5
and 5-3^2=-4
5-2^2=1
2^2-5=-1
3^2-5=4
but if you have to multiply them by 5 as well then (2^2-5)5=-5
→ Solutions
⇒ Simplify <span><span><span>4<span>(<span>2a</span>)</span></span>+<span>7<span>(<span>−<span>4b</span></span>)</span></span></span>+<span><span>3c</span><span>(5)</span></span></span><span>⇒ </span><span><span><span><span><span>8a</span>+</span>−<span>28b</span></span>+<span>15<span>c
Answer
</span></span></span></span><span>⇒ </span><span>8a−28b</span><span>+</span><span>15c</span>