Rational Functions: Solving Rational Equations and Inequalities

think icon Think & Click: Solving Rational Equations

Solve: 1 divided by x plus one-third equals 8 divided by 3 x

3 x times the sum 1 divided by x plus one-third equals 8 divided by 3 x times 3x, 3 plus x equals 8, x equals 5

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Solve: the quantity x minus 10 divided by the quantity 2x plus 1 equals 4x divided by the quantity 3 x plus 4

the quantity 2 x plus 1 times the quantity 3 x plus 4 times the quantity x minus 10 divided by the quantity 2x plus 1 equals 4x divided by the quantity 3 x plus 4 times the quantity 2 x plus 1 times the quantity 3 x plus 4, the quantity 3 x plus 4 times the quantity x minus 10 equals 4 x times the quantity 2 x plus 1, 3 x squared minus 30 x plus 4 x minus 40 equals 8 x squared plus 4 x, negative 5 x squared minus 26 x minus 40 equals 4 x, negative 5 x squared minus 30 x minus 40 equals 0, negative 5 times the quantity x squared plus 6 x plus 8 equals 0, x squared plus 6 x plus 8 equals 0, the quantity x plus 2 times the quantity x plus 4 equals 0, x equals negative 2 or x equals negative 4

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