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1/x + 1/x-3 = x-2/x-3

User Fake Jim
by
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1 Answer

3 votes

Step 1: Multiply both sides by x.

−3x+2=x2−3x−2

Step 2: Multiply both sides by x.

−3x2+2x=x3−3x2−2x

−3x2+2x−(x3−3x2−2x)=x3−3x2−2x−(x3−3x2−2x)(Subtract x^3-3x^2-2x from both sides)

−x3+4x=0

x(−x+2)(x+2)=0(Factor left side of equation)

x=0 or −x+2=0 or x+2=0(Set factors equal to 0)

x=0 or x=2 or x=−2

Check answers. (Plug them in to make sure they work.)

x=2(Works in original equation)

x=−2(Works in original equation)

User Mate Hegedus
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