$\frac{13}{2 x} - \frac{4}{15} = \frac{31}{6 x}$

Answer

$x_{1} = 0 x_{2} = \frac{1}{5}$

Explanation

\frac{13}{2 x} - \frac{4}{15} 2 x \cdot 15 \cdot 6 \cdot \frac{13}{2 x} - 2 x \cdot 15 \cdot 6 \cdot \frac{4}{15} 1170 x^{2} - 48 x 1170 x^{2} - 48 x - 930 x^{2} 240 x^{2} - 48 x = \frac{31}{6 x} = 2 x \cdot 15 \cdot 6 \cdot \frac{31}{6 x} = 930 x^{2} = 0 = 0 multiply ALL terms by 2 x \cdot 15 \cdot 6 . cancel out the denominators move all terms to the left hand side simplify left side

In order to solve $240 x^{2} - 48 x = 0$ , first we need to factor our $x$ .

240 x^{2} - 48 x = x (240 x - 48)

$x = 0$ is a root of multiplicity $1$ .

The second root can be found by solving equation $240 x - 48 = 0$ .

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2x13​−154​=6x31​

x1​=0​x2​=51​​

$\frac{13}{2 x} - \frac{4}{15} = \frac{31}{6 x}$

$x_{1} = 0 x_{2} = \frac{1}{5}$