Question

A²-25/a²-3a:a²+5a/a²-9​

Answer 1

Відповідь:    ( a + 3 )( a - 5 )/a² .

Пояснення:

     ( a²- 25 )/( a²- 3a ) : ( a² + 5a )/( a²- 9 ) = ​( a²- 25 )/( a²- 3a ) Х

    Х ( a²- 9 )/( a² + 5a ) = [(a - 5 )(a + 5 )(a - 3 )(a + 3 )]/[a(a - 3 )*a( a + 5 ) =

    = ( a + 3 )( a - 5 )/a² .

Answer 2

To simplify the expression (A²-25)/(A²-3A):(A²+5A)/(A²-9), we can follow these steps:

Step 1: Factorize the numerator and denominator of each fraction: (A²-25) can be factored as (A-5)(A+5) (A²-3A) cannot be factored further (A²+5A) cannot be factored further (A²-9) can be factored as (A-3)(A+3)

Step 2: Rewrite the expression using the factored forms: [(A-5)(A+5)/(A-3A)] / [(A+5A)/(A-9)]

Step 3: Simplify the expression: [(A-5)(A+5)/(A-3A)] / [(A+5A)/(A-9)] [(A-5)(A+5)/(A-3A)] * [(A-9)/(A+5A)]

Step 4: Simplify further if possible: [(A-5)(A+5)] / [(A-3A)] * [(A-9)/(A+5A)] [(A-5)(A+5)] / [-2A] * [(A-9)/(6A)]

Step 5: Simplify the expression and cancel out common factors: [(A-5)(A+5)(A-9)] / [-2A * 6A] [(A-5)(A+5)(A-9)] / [-12A^2]

Therefore, the simplified form of the expression (A²-25)/(A²-3A):(A²+5A)/(A²-9) is (A-5)(A+5)(A-9)/(-12A^2).