Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2x2−4x−21
Evaluate
(1−4x−1−21x−2)
Evaluate
1−4x−1−21x−2
Rewrite the expression
More Steps
Evaluate
−4x−1
Express with a positive exponent using a−n=an1
−4×x1
Rewrite the expression
x−4
Use b−a=−ba=−ba to rewrite the fraction
−x4
1−x4−21x−2
Rewrite the expression
More Steps
Evaluate
−21x−2
Express with a positive exponent using a−n=an1
−21×x21
Rewrite the expression
x2−21
Use b−a=−ba=−ba to rewrite the fraction
−x221
1−x4−x221
Reduce fractions to a common denominator
x×xx×x−x×x4x−x221
Multiply the terms
x2x×x−x×x4x−x221
Multiply the terms
x2x×x−x24x−x221
Write all numerators above the common denominator
x2x×x−4x−21
Solution
x2x2−4x−21
Show Solution
Find the roots
x1=−3,x2=7
Evaluate
(1−4x−1−21x−2)
To find the roots of the expression,set the expression equal to 0
1−4x−1−21x−2=0
Find the domain
1−4x−1−21x−2=0,x=0
Calculate
1−4x−1−21x−2=0
Rewrite the expression
More Steps
Evaluate
−4x−1
Express with a positive exponent using a−n=an1
−4×x1
Rewrite the expression
x−4
Use b−a=−ba=−ba to rewrite the fraction
−x4
1−x4−21x−2=0
Rewrite the expression
More Steps
Evaluate
−21x−2
Express with a positive exponent using a−n=an1
−21×x21
Rewrite the expression
x2−21
Use b−a=−ba=−ba to rewrite the fraction
−x221
1−x4−x221=0
Multiply both sides of the equation by LCD
(1−x4−x221)x2=0×x2
Simplify the equation
More Steps
Evaluate
(1−x4−x221)x2
Apply the distributive property
1×x2−x4×x2−x221×x2
Simplify
1×x2−4x−21
Any expression multiplied by 1 remains the same
x2−4x−21
x2−4x−21=0×x2
Any expression multiplied by 0 equals 0
x2−4x−21=0
Factor the expression
More Steps
Evaluate
x2−4x−21
Rewrite the expression
x2+(3−7)x−21
Calculate
x2+3x−7x−21
Rewrite the expression
x×x+x×3−7x−7×3
Factor out x from the expression
x(x+3)−7x−7×3
Factor out −7 from the expression
x(x+3)−7(x+3)
Factor out x+3 from the expression
(x−7)(x+3)
(x−7)(x+3)=0
When the product of factors equals 0,at least one factor is 0
x−7=0x+3=0
Solve the equation for x
More Steps
Evaluate
x−7=0
Move the constant to the right-hand side and change its sign
x=0+7
Removing 0 doesn't change the value,so remove it from the expression
x=7
x=7x+3=0
Solve the equation for x
More Steps
Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0−3
Removing 0 doesn't change the value,so remove it from the expression
x=−3
x=7x=−3
Check if the solution is in the defined range
x=7x=−3,x=0
Find the intersection of the solution and the defined range
x=7x=−3
Solution
x1=−3,x2=7
Show Solution