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

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

Answer

Explanation:

Step1: Distribute on the left - hand side

$(3x)(x - 2)\frac{x + 2}{3x}-(3x)(x - 2)\frac{1}{x - 2}=(x - 2)(x + 2)-3x$ Using the difference of squares formula $(a - b)(a + b)=a^{2}-b^{2}$, we have $x^{2}-4-3x$.

Step2: Distribute on the right - hand side

$(3x)(x - 2)\frac{x - 3}{3x}=(x - 2)(x - 3)$ Expand $(x - 2)(x - 3)$ using FOIL method: $x^{2}-3x-2x + 6=x^{2}-5x + 6$.

Step3: Set up the resulting equation

$x^{2}-4-3x=x^{2}-5x + 6$

Answer:

$x^{2}-4-3x=x^{2}-5x + 6$