Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
y2−16y4x+9y4
Evaluate
y2−16x2−81÷y4x−9
Multiply by the reciprocal
y2−16x2−81×x−9y4
Rewrite the expression
y2−16(x−9)(x+9)×x−9y4
Cancel out the common factor x−9
y2−16x+9×y4
Multiply the terms
y2−16(x+9)y4
Multiply the terms
y2−16y4(x+9)
Solution
More Steps
Evaluate
y4(x+9)
Apply the distributive property
y4x+y4×9
Use the commutative property to reorder the terms
y4x+9y4
y2−16y4x+9y4
Show Solution
Find the excluded values
y=4,y=−4,y=0,x=9
Evaluate
y2−16x2−81÷y4x−9
To find the excluded values,set the denominators equal to 0
y2−16=0y4=0y4x−9=0
Solve the equations
More Steps
Evaluate
y2−16=0
Move the constant to the right-hand side and change its sign
y2=0+16
Removing 0 doesn't change the value,so remove it from the expression
y2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±16
Simplify the expression
More Steps
Evaluate
16
Write the number in exponential form with the base of 4
42
Reduce the index of the radical and exponent with 2
4
y=±4
Separate the equation into 2 possible cases
y=4y=−4
y=4y=−4y4=0y4x−9=0
The only way a power can be 0 is when the base equals 0
y=4y=−4y=0y4x−9=0
Solve the equations
More Steps
Evaluate
y4x−9=0
Cross multiply
x−9=y4×0
Simplify the equation
x−9=0
Move the constant to the right side
x=0+9
Removing 0 doesn't change the value,so remove it from the expression
x=9
y=4y=−4y=0x=9
Solution
y=4,y=−4,y=0,x=9
Show Solution