$\frac{19}{4 x} + \frac{2}{3} = \frac{11}{4 x}$

Answer

$x_{1} = 0 x_{2} = - \frac{1}{3}$

Explanation

\frac{19}{4 x} + \frac{2}{3} 4 x \cdot 3 \cdot \frac{19}{4 x} + 4 x \cdot 3 \cdot \frac{2}{3} 57 x^{2} + 8 x 57 x^{2} + 8 x - 33 x^{2} 24 x^{2} + 8 x = \frac{11}{4 x} = 4 x \cdot 3 \cdot \frac{11}{4 x} = 33 x^{2} = 0 = 0 multiply ALL terms by 4 x \cdot 3 . cancel out the denominators move all terms to the left hand side simplify left side

In order to solve $24 x^{2} + 8 x = 0$ , first we need to factor our $x$ .

24 x^{2} + 8 x = x (24 x + 8)

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

The second root can be found by solving equation $24 x + 8 = 0$ .

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4x19​+32​=4x11​

x1​=0​x2​=−31​​

$\frac{19}{4 x} + \frac{2}{3} = \frac{11}{4 x}$

$x_{1} = 0 x_{2} = - \frac{1}{3}$