Answer:
[tex] \frac{( {x} + 1) (x - 1)(16 {x} - 37)}{( {x}^{2} + 2)}[/tex]
Step-by-step explanation:
[tex] \frac{ \frac{3 {x}^{2} - 3 }{x} }{ \frac{3( {x}^{2} + 2)}{16 {x}^{2} - 37x } \\ \\ = \frac{3( {x}^{2} - 1) }{x} \times \frac{x(16 {x} } - 37)}{3( {x}^{2} + 2)} \\ \\ = \frac{3( {x} + 1) (x - 1)}{x} \times \frac{x(16 {x} - 37)}{3( {x}^{2} + 2)} \\ \\ = \frac{( {x} + 1) (x - 1)}{1} \times \frac{(16 {x} - 37)}{( {x}^{2} + 2)} \\ \\ = \frac{( {x} + 1) (x - 1)(16 {x} - 37)}{( {x}^{2} + 2)}[/tex]
Answer:
C
Step-by-step explanation:
Simplify the numerator/ denominator
[tex]\frac{3x^2-3}{x}[/tex] ← factor out 3 from each term on the numerator
= [tex]\frac{3(x^2-1)}{x}[/tex] ← factor (x² - 1) as a difference of squares
= [tex]\frac{3(x+1)(x-1)}{x}[/tex]
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[tex]\frac{3(x^2+2)}{16x^2-37x}[/tex] ← factor out x from each term on the denominator
= [tex]\frac{3(x^2+2)}{x(16x-37)}[/tex]
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[tex]\frac{3(x+1)(x-1)}{x}[/tex] ÷ [tex]\frac{3(x^2+2)}{x(16x-37)}[/tex]
To divide the expressions
Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is
[tex]\frac{3(x+1)(x-1)}{x}[/tex] × [tex]\frac{x(16x-37)}{3(x^2+2)}[/tex]
Cancel the x's and the 3's on the numerator/ denominator, leaving
[tex]\frac{(x+1)(x-1)(16x-37)}{x^2+2}[/tex] → C
