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

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Answer 1 · 2018-05-11T03:24:18

#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#