Algebra
Calculus
Trigonometry
Matrix
Question
Find the excluded values
x=0
Evaluate
x3x2−17
To find the excluded values,set the denominators equal to 0
x3=0
Solution
x=0
Show Solution
Rewrite the fraction
−x317+x1
Evaluate
x3x2−17
For each factor in the denominator,write a new fraction
x3?+x2?+x?
Write the terms in the numerator
x3A+x2B+xC
Set the sum of fractions equal to the original fraction
x3x2−17=x3A+x2B+xC
Multiply both sides
x3x2−17×x3=x3A×x3+x2B×x3+xC×x3
Simplify the expression
x2−17=1×A+xB+x2C
Any expression multiplied by 1 remains the same
x2−17=A+xB+x2C
Group the terms
x2−17=Cx2+Bx+A
Equate the coefficients
⎩⎨⎧1=C0=B−17=A
Swap the sides
⎩⎨⎧C=1B=0A=−17
Find the intersection
⎩⎨⎧A=−17B=0C=1
Solution
−x317+x1
Show Solution
Find the roots
x1=−17,x2=17
Alternative Form
x1≈−4.123106,x2≈4.123106
Evaluate
x3x2−17
To find the roots of the expression,set the expression equal to 0
x3x2−17=0
The only way a power can not be 0 is when the base not equals 0
x3x2−17=0,x=0
Calculate
x3x2−17=0
Cross multiply
x2−17=x3×0
Simplify the equation
x2−17=0
Move the constant to the right side
x2=17
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±17
Separate the equation into 2 possible cases
x=17x=−17
Check if the solution is in the defined range
x=17x=−17,x=0
Find the intersection of the solution and the defined range
x=17x=−17
Solution
x1=−17,x2=17
Alternative Form
x1≈−4.123106,x2≈4.123106
Show Solution