x/3+(x^2)/4 =(5x)/6 — step-by-step solution

Let's solve in

ℝ

\frac{x}{3} + \frac{x^{2}}{4} = \frac{5 x}{6}

Let's sum the fractions:

\frac{x}{3} + \frac{x^{2}}{4} - \frac{5 x}{6} = 0

ⓘ Like terms are grouped by adding their coefficients:

\frac{x}{3} - \frac{5 x}{6}

- \frac{x}{2}

■To add fractions, put them over the same denominator, then add the numerators:

- \frac{x}{2} + \frac{x^{2}}{4}

\frac{- x \cdot 2 + x^{2}}{4}

\frac{- x \cdot 2 + x^{2}}{4} = 0

ⓘ What the terms have in common is factored out, so that the fraction can be simplified:

\frac{- x \cdot 2 + x^{2}}{4}

\frac{x \cdot (- 2 + x)}{4}

\frac{x \cdot (- 2 + x)}{4} = 0

⇥Let's solve in

ℝ

x \cdot (- 2 + x) = 0

⇥A product is zero if and only if one of its factors is zero: we solve each factor equal to 0

⇥⇥Let's solve in

ℝ

x = 0

⇥⇥Solution found:

x = 0

⇥⇥Let's solve in

ℝ

- 2 + x = 0

⇥⇥Solution obtained:

x = 2

▶Solution:

x = {0, 2}