Algebra
Calculus
Trigonometry
Matrix
Question :
(x^2-x-1)/((x-1))=(1-x)/((x-1))
Solve the equation
x1=−2,x2=2
Alternative Form
x1≈−1.414214,x2≈1.414214
Evaluate
(x−1)(x2−x−1)=(x−1)(1−x)
Find the domain
More Steps
Evaluate
x−1=0
Move the constant to the right side
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
(x−1)(x2−x−1)=(x−1)(1−x),x=1
Remove the parentheses
x−1x2−x−1=x−11−x
Cross multiply
(x2−x−1)(x−1)=(x−1)(1−x)
Simplify the equation
(x2−x−1)(x−1)=−(x−1)2
Expand the expression
More Steps
Evaluate
(x2−x−1)(x−1)
Apply the distributive property
x2×x−x2×1−x×x−(−x×1)−x−(−1)
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−x2×1−x×x−(−x×1)−x−(−1)
Any expression multiplied by 1 remains the same
x3−x2−x×x−(−x×1)−x−(−1)
Multiply the terms
x3−x2−x2−(−x×1)−x−(−1)
Any expression multiplied by 1 remains the same
x3−x2−x2−(−x)−x−(−1)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−x2−x2+x−x+1
Subtract the terms
More Steps
Evaluate
−x2−x2
Collect like terms by calculating the sum or difference of their coefficients
(−1−1)x2
Subtract the numbers
−2x2
x3−2x2+x−x+1
The sum of two opposites equals 0
More Steps
Evaluate
x−x
Collect like terms
(1−1)x
Add the coefficients
0×x
Calculate
0
x3−2x2+0+1
Remove 0
x3−2x2+1
x3−2x2+1=−(x−1)2
Expand the expression
More Steps
Evaluate
−(x−1)2
Expand the expression
More Steps
Evaluate
(x−1)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×1+12
Calculate
x2−2x+1
−(x2−2x+1)
Expand the expression
−x2+2x−1
x3−2x2+1=−x2+2x−1
Move the expression to the left side
x3−2x2+1−(−x2+2x−1)=0
Calculate the sum or difference
More Steps
Evaluate
x3−2x2+1−(−x2+2x−1)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−2x2+1+x2−2x+1
Add the terms
More Steps
Evaluate
−2x2+x2
Collect like terms by calculating the sum or difference of their coefficients
(−2+1)x2
Add the numbers
−x2
x3−x2+1−2x+1
Add the numbers
x3−x2+2−2x
x3−x2+2−2x=0
Factor the expression
(x−1)(x2−2)=0
Separate the equation into 2 possible cases
x−1=0x2−2=0
Solve the equation
More Steps
Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=1x2−2=0
Solve the equation
More Steps
Evaluate
x2−2=0
Move the constant to the right-hand side and change its sign
x2=0+2
Removing 0 doesn't change the value,so remove it from the expression
x2=2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±2
Separate the equation into 2 possible cases
x=2x=−2
x=1x=2x=−2
Check if the solution is in the defined range
x=1x=2x=−2,x=1
Find the intersection of the solution and the defined range
x=2x=−2
Solution
x1=−2,x2=2
Alternative Form
x1≈−1.414214,x2≈1.414214
Show Solution
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