Question

x-3/x=2 find the roots​

Answer 1

Factor

1.Find common denominator

$\tt x + \frac{ - 3}{x} = 2$

$\tt \frac{xx}{x} + \frac{ - 3}{x} = 2$

2. Combine fractions with common denominator

$\sf \frac{xx - 3}{x} = 2$

3.Combine exponents

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$\tt\frac{x² - 3}{x} = 2$

4.Multiply all terms by the same value to eliminate fraction denominators

$\tt \: x. \frac{x² - 3}{x} = x.2$

5.Cancel multiplied terms that are in the denominator

$\tt \: {x}^{2} - 3 = x.2$

6.Re-order terms so that constants are on the left

$\tt \: x² - 3 = 2x$

7.Move terms to the left side

$\tt \: x² - 3 - 2x = 0$

8.Rearrange terms

$\tt \: x² = 2x - 3 = 0$

9.Use the sum-product pattern

Identify a, b and c in your equation and then find two numbers that when multiplied together equal c, and when added together equal b.

$\tt \: x² - 2x - 3 = 0$

10.Factor

Write your equation in factored form

$\tt(x - 3)(x + 1) = 0$

11.Create two separate equations

Set each factor equal to zero

$\tt \: x - 3 = 0$

$\tt \: x + 1 = 0$

12.Solve

Rearrange and isolate the variable to find each solution

$\tt \color {red}x = 3 \tt \\ \tt \color{red} x = - 1$

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