Question

Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the variable.

Answer 1

(x² + 4x - 45)/(x² + 10x + 9) 

Numerator = N = x² + 4x - 45 
= x² + 9x - 5x - 45 
= (x² + 9x) - (5x + 45) 
= x(x + 9) - 5(x + 9) 
= (x + 9)(x - 5) 

Denominator = D = x² + 10x + 9 
= x² + x + 9x + 9 
= (x² + x) + (9x + 9) 
= x(x + 1) + 9(x + 1) 
= (x + 1)(x + 9) 

Hence, the given expr. = N/D 
= {(x + 9)(x - 5)}/{(x + 1)(x + 9) 
= (x - 5)/(x + 1) 

Restrictions : x ≠ - 1, x = 5 


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Answer 2

Answer:

quantity x plus 5 over x plus 1 , x ≠ −1, x ≠ 5

Step-by-step explanation: