How do you solve the rational equation # 5 /( x+4) = 4 + 3/ (x-2)#?

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Answer 1 · 2016-01-31T21:37:23

You must put everything on the same denominator and then solve the resulting quadratic equation.

The Least Common Denominator (LCM) would be (x + 4)(x - 2)

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

5x - 10 = 4(#x^2# + 4x - 2x - 8) + 3x + 12

5x - 10 = #4x^2# + 8x - 32 + 3x + 12

0 = #4x^2# + 6x - 10

0 = 2(#2x^2# + 3x - 5)

0 = 2(#2x^2# + 5x - 2x - 5)

0 = 2(x(2x + 5) - (1(2x + 5))

0 = 2(x - 1)(2x + 5)

x = 1 and #-5/2#

Your solution set is x = 1 and #-5/2#