By simplifying ![\[x - \frac{{23}}{{{x^2}}} - x - 20 - \frac{2}{5} - x\]](https://tex.z-dn.net/?f=%5C%5Bx%20-%20%5Cfrac%7B%7B23%7D%7D%7B%7B%7Bx%5E2%7D%7D%7D%20-%20x%20-%2020%20-%20%5Cfrac%7B2%7D%7B5%7D%20-%20x%5C%5D)
. This will result in a simplified version of ![\[ - \frac{{5{x^3} + 102{x^2} + 115}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%20-%20%5Cfrac%7B%7B5%7Bx%5E3%7D%20%2B%20102%7Bx%5E2%7D%20%2B%20115%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
.
The Simplifying Algorithm is a wonderful way to simplify complex mathematics problems. It can be used to solve equations, convert fractions to decimals, and perform many other math operations. In this problem, the Simplifying Algorithm will help you reduce
Since two opposites add up to 0, remove them from the expression.
![\[ - \frac{{23}}{{{x^2}}} - \frac{{102}}{5} - x\]](https://tex.z-dn.net/?f=%5C%5B%20-%20%5Cfrac%7B%7B23%7D%7D%7B%7B%7Bx%5E2%7D%7D%7D%20-%20%5Cfrac%7B%7B102%7D%7D%7B5%7D%20-%20x%5C%5D)
Write all numerators above the least common denominator 5x2
![\[ - \frac{{115 + 102{x^2} + 5{x^3}}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%20-%20%5Cfrac%7B%7B115%20%2B%20102%7Bx%5E2%7D%20%2B%205%7Bx%5E3%7D%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
Use the commutative property to reorder the terms so that constants on the left
![\[\frac{{ - 5{x^3} - 115 - 102{x^2}}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B%7B%20-%205%7Bx%5E3%7D%20-%20115%20-%20102%7Bx%5E2%7D%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
Rearrange the terms
![\[\frac{{ - 5{x^3} - 102{x^2} - 115}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B%7B%20-%205%7Bx%5E3%7D%20-%20102%7Bx%5E2%7D%20-%20115%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
By reording the terms
Hence, by simplifying this equation, divide both numerator and denominator. This will result in a simplified version of .
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#2) Use quotient rule
Remember for solving log equations:
#3) Derivative of tan = sec^2 = 1/cos^2
Domain of tan is [-pi/2, pi/2], only consider x values in that domain.
#4 Use Quotient rule
#9 Use double angle identity for tan
This way you can rewrite tan(pi/2) in terms of tan(pi/4).
Next use L'hopitals rule, which says the limit of indeterminate form(0/0) equals limit of quotient of derivatives of top/bottom of fraction.
Take derivative of both top part and bottom part separately, then reevaluate the limit. <span />
<h3>Given</h3>
... f(x) = x² -4x +1
<h3>Find</h3>
... a) f(-8)
... b) f(x+9)
... c) f(-x)
<h3>Solution</h3>
In each case, put the function argument where x is, then simplify.
a) f(-8) = (-8)² -4(-8) +1 = 64 +32 + 1 = 97
b) f(x+9) = (x+9)² -4(x+9) +1
... = x² +18x +81 -4x -36 +1
... f(x+9) = x² +14x +46
c) f(-x) = (-x)² -4(-x) +1
... f(-x) = x² +4x +1
70 times .9 is 63 so 90 minus 63 is27 so it was $27
