Question

Сократите дробь 4x+3/4x^2-5x-6

Answer 1

$\frac{4x+3}{4x^{2}-5x-6}; \\ 1) 4x^{2}-5x-6 = 0 \\ \frac{4}{4}x^{2}-5x-6*4 = 0 \\ x = a \\ a^{2}-5a-24=0 \\ a1 = 8 \\ a2 = -3 \\ x1 = \frac{8}{4} = 2; \\ x2 = - \frac{3}{4} . \\ 4x^{2}-5x-6 = 4(x-2)(x+ \frac{3}{4} ) \\ 2) 4x+3 = 4(x+ \frac{3}{4} )$

So...

$\frac{4(x+ \frac{3}{4})}{4(x-2)(x+ \frac{3}{4})} = \frac{1}{x-2}$

Answort :  $\frac{1}{x-2}$

Answer 2

 4x^2 - 5x - 6 = 4( x + 0,75 )( x - 2 ) = ( 4x + 3 )( x - 2 )
D = 25 + 96 = 121 = 11^2 
x1 = ( 5 + 11 ) : 8 = 2 
x2 = ( 5 - 11 ) : 8 = - 0,75
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( 4x + 3 ) / ( ( 4x + 3 )( x - 2 )) = 1 / ( x - 2 )