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alexandr402 [8]
3 years ago
15

See attachment the problem can be found in there

Mathematics
1 answer:
zloy xaker [14]3 years ago
7 0

Answer:

\frac{ - 2 {x}^{2}  + 19x   + 3 }{3 {x} (4x^{2}     -  9 )}

Step-by-step explanation:

\frac{5}{6 {x}^{2}  + 9x}  +  \frac{1}{2x - 3}  -  \frac{2}{3x}  \\  \\  =  \frac{5}{3x(2 {x}   + 3)}  +  \frac{1}{2x - 3}  -  \frac{2}{3x}  \\  \\ =  \frac{5(2x - 3) + 1 \times 3x(2x + 3)}{3x(2 {x}   + 3)(2x - 3)}  -  \frac{2}{3x}  \\  \\  = \frac{10x - 15 + 6 {x}^{2}  + 9x}{3x((2 {x} ) ^{2}     -  {3}^{2} )}  -  \frac{2}{3x} \\  \\  = \frac{6 {x}^{2}   + 19x - 15}{3x(4x^{2}     -  9 )}  -  \frac{2}{3x} \\  \\  = \frac{3x(6 {x}^{2}   + 19x - 15) - 2 \times 3x(4x^{2}     -  9 )}{3x(4x^{2}     -  9 ) \times 3x}  \\  \\  = \frac{18{x}^{3}   + 57 {x}^{2}  - 45x - 24x^{3}      + 54x }{3x(4x^{2}     -  9 ) \times 3x}   \\  \\ = \frac{ - 6 {x}^{3}  + 57 {x}^{2}   + 9x }{9 {x}^{2} (4x^{2}     -  9 )}  \\  \\ = \frac{ 3x(- 2 {x}^{2}  + 19x   + 3) }{9 {x}^{2} (4x^{2}     -  9 )}  \\  \\  \huge \orange{ \boxed{= \frac{ - 2 {x}^{2}  + 19x   + 3 }{3 {x} (4x^{2}     -  9 )}  }}

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