-2 x+4 ----- = ------ x+2 x^2-4

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-2 x+4 ----- = ------ x+2 x^2-4

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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A. x=0, -2 B. x=0,2,-2 C.x=2,-2 D.x=0
A. x=0, -2
Solve for x over the real numbers: -2/(x+2) = (x+4)/(x^2-4) Multiply both sides by a polynomial to clear fractions. Cross multiply: -2 (x^2-4) = (x+2) (x+4) Write the quadratic polynomial on the left hand side in standard form. Expand out terms of the left hand side: 8-2 x^2 = (x+2) (x+4) Write the quadratic polynomial on the right hand side in standard form. Expand out terms of the right hand side: 8-2 x^2 = x^2+6 x+8 Move everything to the left hand side. Subtract x^2+6 x+8 from both sides: -6 x-3 x^2 = 0 Factor the left hand side. Factor x and constant terms from the left hand side: -3 x (x+2) = 0 Divide both sides by a constant to simplify the equation. Divide both sides by -3: x (x+2) = 0 Solve each term in the product separately. Split into two equations: x = 0 or x+2 = 0 Look at the second equation: Solve for x. Subtract 2 from both sides: x = 0 or x = -2 Now test that these solutions are correct by substituting into the original equation. Check the solution x = -2. -2/(x+2) => -2/(2-2) = infinity^~ ~~ infinity^~ (x+4)/(x^2-4) => (4-2)/(4-4) = infinity^~ ~~ infinity^~: So this solution is incorrect Check the solution x = 0. -2/(x+2) => -2/(2+0) = -1 (x+4)/(x^2-4) => (4+0)/(0-4) = -1: So this solution is correct Gather any correct solutions. The solution is: Answer: x = 0

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(x+2)*(x+4)=(x^2-4)*(-2) x^2+4x+2x+8=-2x^2+8 3x^2+6x=0 delta=6^2-4*3*0=36 x1,2=[-6+-sqrt(delta)]/6 so x1=0 and x2=-2 so A is the correct answer

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