Question

Solve this quadratic equation without using the quadratic formula. Use zero-product rule instead.​

Answer 1

Answer:

For a quadratic equation $\frac{6}{x}- \frac{2}{(x-1)} =\frac{1}{(x-2)}$

x$=\frac{4}{3}$ or x = 3

Step-by-step explanation:



Given

$\frac{6}{x}- \frac{2}{(x-1)} =\frac{1}{(x-2)} \\\\\frac{6(x-1)-2x}{x(x-1)} =\frac{1}{(x-2)} \\\\\frac{6x-6-2x}{x^{2} -x} =\frac{1}{(x-2)} \\\\(4x-6)(x-2)=x^{2} -x\\4x^{2} -8x-6x+12= x^{2} -x\\4x^{2} -x^{2} -14x+x+12=0\\\\3x^{2} -13x+12=0$

So the quadratic equation is $3x^{2} -13x+12=0$

Inorder to solve using zero product rule,

we can split -13$x$ as -9x-4x

That is $3x^{2} -13x+12= 3x^{2} -9x-4x+12$

Therefore $3x^{2} -9x-4x+12=0$

$3x(x-3)-4(x-3)=0\\\\(3x-4)(x-3)=0$

Therefore

$(3x-4)=0\\\\3x=4\\\\x=\frac{4}{3} \\\\Also, \\\\(x-3)=0\\\\ x= 3$

So x= $\frac{4}{3}$ or x = 3