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How do you solve the rational equation #(2x)/(x+4)=3/(x-1)#?

Answer 1

Hazel Anglin

#color(blue)(x = 4, -3/2#

#(2x) / (x + 4) = 3 / (x - 1)#

#2x * (x - 1) = 3 * (x + 4), " cross multiplying"#

#2x^2 - 2x = 3x + 12, " removing braces"#

#2x^2 -2x - 3x - 12 = 0, " bringing all terms to L H S"#

#2x^2 - 5x - 12 = 0, " simplifying"#

#2x^2 - 8x + 3x - 12 = 0#

#2x (x - 4) + 3* (x - 4) = 0#

#(x - 4) * (2x + 3) = 0#

#color(blue)(x = 4, -3/2#

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Answer 2

Hazel Anglin

To solve the rational equation (2x)/(x+4)=3/(x-1), you can start by cross-multiplying to eliminate the fractions. This gives you 2x(x-1) = 3(x+4). Expanding and simplifying the equation, you get 2x^2 - 2x = 3x + 12. Rearranging the terms, you have 2x^2 - 5x - 12 = 0. To solve this quadratic equation, you can factor it as (2x + 3)(x - 4) = 0. Setting each factor equal to zero, you find two possible solutions: x = -3/2 and x = 4. Therefore, the solutions to the rational equation are x = -3/2 and x = 4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.