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put this solution on YOUR website!(x^(2)-16)/(x^(2)-2x-8)*x=(2)/(x^(2))
ALL ~ signs stand for the square root of and the / signs mean +-
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
((x-4)(x+4))/(x^(2)-2x-8)*x=(2)/(x^(2))
In this problem 2*-4=-8 and 2-4=-2, so insert 2 as the right hand term of one factor and -4 as the right-hand term of the other factor.
((x-4)(x+4))/((x+2)(x-4))*x=(2)/(x^(2))
Reduce the expression by canceling out the common factor of (x-4) from the numerator and denominator.
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(x-4)(x+4))/((x+2)(x-4))*x=(2)/(x^(2))
Reduce the expression by canceling out the common factor of (x-4) from the numerator and denominator.
(x+4)/(x+2)*x=(2)/(x^(2))
Multiply the rational expressions to get (x(x+4))/((x+2)).
(x(x+4))/(x+2)=(2)/(x^(2))
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
x(x+4)*x^(2)=2*(x+2)
Multiply x by x^(2) to get x^(3).
x^(3)(x+4)=2*(x+2)
Multiply 2 by each term inside the parentheses.
x^(3)(x+4)=2x+4
Multiply x^(3) by each term inside the parentheses.
x^(4)+4x^(3)=2x+4
Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.
x^(4)+4x^(3)-2x=4
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
x^(4)+4x^(3)-2x-4=0
Use the quadratic formula to find the solutions. In this case, the values are a=1, b=4, and c=-2-4.
x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0
Use the standard form of the equation to find a, b, and c for this quadratic.
a=1, b=4, and c=-2-4
Substitute in the values of a=1, b=4, and c=-2-4.
x=(-4\~((4)^(2)-4(1)(-2-4)))/(2(1))
Simplify the section inside the radical.
x=(-4\2~(10))/(2(1))
Simplify the denominator of the quadratic formula.
x=(-4\2~(10))/(2)
First, solve the + portion of \.
x=(-4+2~(10))/(2)
Simplify the expression to solve for the + portion of the \.
x=-2+~(10)
Next, solve the - portion of \.
x=(-4-2~(10))/(2)
Simplify the expression to solve for the - portion of the \.
x=-2-~(10)
The final answer is the combination of both solutions.
x=-2+~(10),-2-~(10)
Verify each of the first set of solutions by substituting them into the original equation and solving. In this case, none of the solutions are valid.
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