Question

What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x minus 2 ?

Answer 1

Answer:

The simplified form is : 1 / ( x + 3 )( x + 4 )

Step-by-step explanation:

( x + 1 ) / ( x² + x - 6 )  :  ( x² + 5 x + 4 ) / ( x - 2 ) =

= ( x + 1 ) / ( x + 3 )( x - 2 )  :  ( x + 4 ) ( x + 1 ) / ( x - 2 ) =

= ( x + 1 ) / ( x + 3 ) ( x - 2 ) · ( x - 2 ) / ( x + 4 ) ( x + 1 ) =

(after cancelling) = 1 / ( x + 3 ) ( x + 4 ).

Answer 2

Answer:

Simplified form of given statement in the question is  $\frac{1 }{ ( x + 3 ) ( x + 4 ) }$

That is,

1 over  x plus 3  mutliplied with x plus 4

Step-by-step explanation:

x plus 1 = x + 1

x squared plus x minus 6 = x² + x - 6

x plus 1 over x squared plus x minus 6 = $\frac{x + 1}{ x^{2}+ x - 6}$

Similarly,

x squared plus 5x plus 4 = x² + 5x + 4

x minus 2 = x - 2

x squared plus 5x plus 4 over x minus 2 = $\frac{x^{2} + 5x + 4}{ x - 2 }$

Now,

According to question,

= $\frac{x + 1}{ x^{2} + x - 6}$ / $\frac{x^{2} + 5x + 4}{ x - 2 }$

= $\frac{x + 1}{ x^{2} + 3x - 2x - 6}$ /  $\frac{x^{2} + 4x + x + 4}{ x - 2 }$

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

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

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

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

Hence,

Simplified form of given statement in the question is  $\frac{1 }{ ( x + 3 ) ( x + 4 ) }$

That is,

1 over  x plus 3  mutliplied with x plus 4