Mathematics: What are the real roots of this equation? 12/x-6+x=3+8x/x-6 a) x = 6 b) x = 7.04 and x = 1.095 c) x = 15 and x = 2 d) x = 15

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What are the real roots of this equation? 12/x-6+x=3+8x/x-6

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11.03.2022

ANSWER

The correct answer is $x=15\:or\:x=2$

EXPLANATION

We have the equation;

$\frac{12}{x-6}+x=3+ \frac{8x}{x-6}$

We multiply through by the least common multiple, which is (x-6) .

This gives us;

$(x-6) \times \frac{12}{x-6}+x(x-6)=3(x-6)+ \frac{8x}{x-6} \times (x-6)$

We simplify to obtain;

12+x(x-6)=3(x-6)+ 8x

We now expand to obtain;

12+x^2-6x=3x-18+ 8x

We rewrite the above equation as a quadratic equation in .

This implies that

x^2-6x-3x-8x+12+18=0

This simplifies to;

x^2-17x+30=0

We now split the middle term to obtain;

x^2-15x-2x+30=0

We factor to obtain;

x(x-15)-2(x-15)=0

(x-15)(x-2)=0

$(x-15)=0\:or\:(x-2)=0$

$x=15\:or\:x=2$

Therefore the correct answer is option C

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