the following equation is being multiplied by the lcd. complete the multiplication to eliminate the…

the following equation is being multiplied by the lcd. complete the multiplication to eliminate the denominators.\n$\frac{x + 2}{3x}-\frac{1}{x - 2}=\frac{x - 3}{3x}$\n$(3x)(x - 2)\frac{x + 2}{3x}-\frac{1}{x - 2}=(3x)(x - 2)\frac{x - 3}{3x}$\nthe resulting equation is\n$x + 2-1=x - 3$\n$3x(x + 2)-(x - 2)=x - 3$\n$(x - 2)(x + 2)-1=(x - 3)(x - 2)$\n$(x - 2)(x + 2)-3x=(x - 2)(x - 3)$

the following equation is being multiplied by the lcd. complete the multiplication to eliminate the denominators.\n$\frac{x + 2}{3x}-\frac{1}{x - 2}=\frac{x - 3}{3x}$\n$(3x)(x - 2)\frac{x + 2}{3x}-\frac{1}{x - 2}=(3x)(x - 2)\frac{x - 3}{3x}$\nthe resulting equation is\n$x + 2-1=x - 3$\n$3x(x + 2)-(x - 2)=x - 3$\n$(x - 2)(x + 2)-1=(x - 3)(x - 2)$\n$(x - 2)(x + 2)-3x=(x - 2)(x - 3)$

Answer

Answer:

$(x - 2)(x + 2)-3x=(x - 2)(x - 3)$

Explanation:

Step1: Distribute the left - hand side

$(3x)(x - 2)\frac{x + 2}{3x}-(3x)(x - 2)\frac{1}{x - 2}=(x - 2)(x + 2)-3x$

Step2: Distribute the right - hand side

$(3x)(x - 2)\frac{x - 3}{3x}=(x - 2)(x - 3)$

Step3: Combine the results

The resulting equation is $(x - 2)(x + 2)-3x=(x - 2)(x - 3)$