# SOLUTION: x^2-16/x^2-2x-8*x=2/x^2

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 Click here to see ALL problems on Equations Question 346936: x^2-16/x^2-2x-8*x=2/x^2Answer by haileytucki(390)   (Show Source): You can 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. ((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. No Solution