Algebra
Calculus
Trigonometry
Matrix
Question
Find the excluded values
x=0
Evaluate
x3x2−37
To find the excluded values,set the denominators equal to 0
x3=0
Solution
x=0
Show Solution
Rewrite the fraction
−x337+x1
Evaluate
x3x2−37
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
x3x2−37=x3A+x2B+xC
Multiply both sides
x3x2−37×x3=x3A×x3+x2B×x3+xC×x3
Simplify the expression
x2−37=1×A+xB+x2C
Any expression multiplied by 1 remains the same
x2−37=A+xB+x2C
Group the terms
x2−37=Cx2+Bx+A
Equate the coefficients
⎩⎨⎧1=C0=B−37=A
Swap the sides
⎩⎨⎧C=1B=0A=−37
Find the intersection
⎩⎨⎧A=−37B=0C=1
Solution
−x337+x1
Show Solution
Find the roots
x1=−37,x2=37
Alternative Form
x1≈−6.082763,x2≈6.082763
Evaluate
x3x2−37
To find the roots of the expression,set the expression equal to 0
x3x2−37=0
The only way a power can not be 0 is when the base not equals 0
x3x2−37=0,x=0
Calculate
x3x2−37=0
Cross multiply
x2−37=x3×0
Simplify the equation
x2−37=0
Move the constant to the right side
x2=37
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±37
Separate the equation into 2 possible cases
x=37x=−37
Check if the solution is in the defined range
x=37x=−37,x=0
Find the intersection of the solution and the defined range
x=37x=−37
Solution
x1=−37,x2=37
Alternative Form
x1≈−6.082763,x2≈6.082763
Show Solution