Question

Rational equation for x, 3x/x+1 + 4/x-2=3

Answer 1

x = - 10

Explanation:

Express the fractions on the left side as a single fraction.

Multiply the numerator/denominator of the first fraction by (x - 2)

Multiply the numerator/denominator of the second fraction by (x + 1)

`(3x(x-2))/((x+1)(x-2))` +
`(4(x+1))/((x+1)(x-2))` = 3

Distribute the numerators and simplify

`(3x^2-6x+4x+4)/((x+1)(x-2))` = 3 ( cross- multiply )

3x² - 2x + 4 = 3(x+ 1)(x - 2) ← distribute

3x² - 2x + 4 = 3(x² - x - 2)

3x² - 2x + 4 = 3x² - 3x - 6 ( subtract 3x² - 3x from both sides )

x + 4 = - 6 ( subtract 4 from both sides )

x = - 10