Question
Simplify the expression
w52w2−72
Evaluate
w62w3−72w
Factor
w6w(2w2−72)
Solution
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Calculate
w6w
Use the product rule aman=an−m to simplify the expression
w6−11
Subtract the terms
w51
w52w2−72
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Find the excluded values
w=0
Evaluate
w62w3−72w
To find the excluded values,set the denominators equal to 0
w6=0
Solution
w=0
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Rewrite the fraction
−w572+w32
Evaluate
w62w3−72w
For each factor in the denominator,write a new fraction
w6?+w5?+w4?+w3?+w2?+w?
Write the terms in the numerator
w6A+w5B+w4C+w3D+w2E+wF
Set the sum of fractions equal to the original fraction
w62w3−72w=w6A+w5B+w4C+w3D+w2E+wF
Multiply both sides
w62w3−72w×w6=w6A×w6+w5B×w6+w4C×w6+w3D×w6+w2E×w6+wF×w6
Simplify the expression
2w3−72w=1×A+wB+w2C+w3D+w4E+w5F
Any expression multiplied by 1 remains the same
2w3−72w=A+wB+w2C+w3D+w4E+w5F
Group the terms
2w3−72w=Fw5+Ew4+Dw3+Cw2+Bw+A
Equate the coefficients
⎩⎨⎧0=F0=E2=D0=C−72=B0=A
Swap the sides
⎩⎨⎧F=0E=0D=2C=0B=−72A=0
Find the intersection
⎩⎨⎧A=0B=−72C=0D=2E=0F=0
Solution
−w572+w32
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Find the roots
w1=−6,w2=6
Evaluate
w62w3−72w
To find the roots of the expression,set the expression equal to 0
w62w3−72w=0
The only way a power can not be 0 is when the base not equals 0
w62w3−72w=0,w=0
Calculate
w62w3−72w=0
Divide the terms
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Evaluate
w62w3−72w
Factor
w6w(2w2−72)
Reduce the fraction
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Calculate
w6w
Use the product rule aman=an−m to simplify the expression
w6−11
Subtract the terms
w51
w52w2−72
w52w2−72=0
Cross multiply
2w2−72=w5×0
Simplify the equation
2w2−72=0
Move the constant to the right side
2w2=72
Divide both sides
22w2=272
Divide the numbers
w2=272
Divide the numbers
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Evaluate
272
Reduce the numbers
136
Calculate
36
w2=36
Take the root of both sides of the equation and remember to use both positive and negative roots
w=±36
Simplify the expression
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Evaluate
36
Write the number in exponential form with the base of 6
62
Reduce the index of the radical and exponent with 2
6
w=±6
Separate the equation into 2 possible cases
w=6w=−6
Check if the solution is in the defined range
w=6w=−6,w=0
Find the intersection of the solution and the defined range
w=6w=−6
Solution
w1=−6,w2=6
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