Simplify this expression: \(\frac{x^2+6x+5}{x^2-25}\)

x 2 − 25 x 2 + 6 x + 5 ​ = ( ∗ ) ; x 2 − 25  = 0 → x 2  = 25 → x  = − 5 ∧ x  = 5 x 2 + 6 x + 5 = 0 Δ = 6 2 − 4 ⋅ 1 ⋅ 5 = 36 − 20 = 16 ; Δ ​ = 16 ​ = 4 x 1 ​ = 2 ⋅ 1 − 6 − 4 ​ = 2 − 10 ​ = − 5 ; x 2 ​ = 2 ⋅ 1 − 6 + 4 ​ = 2 − 2 ​ = − 1 x 2 + 6 x + 5 = ( x + 5 ) ( x + 1 )
( ∗ ) = ( x − 5 ) ( x + 5 ) ( x + 5 ) ( x + 1 ) ​ = x − 5 x + 1 ​

Answered by Anonymous | 2024-06-10

x 2 − 25 x 2 + 6 x + 5 ​ = ( x − 5 ) ( x + 5 ) x 2 + 6 x + 5 ​ = ( ∗ ) . x − 5  = 0 an d x + 5  = 0 ⇒ x ∈ R ∖ { 5 ; − 5 } x 2 + 6 x + 5 = ( x + 5 ) ( x + 1 ) b ec a u se : Δ = 6 2 − 4 ⋅ 1 ⋅ 5 = 36 − 20 = 16 ⇒ Δ ​ = 16 ​ = 4 x 1 ​ = 2 ⋅ 1 − 6 − 4 ​ = 2 − 10 ​ = − 5 , x 2 ​ = 2 ⋅ 1 − 6 + 4 ​ = 2 − 2 ​ = − 1 ( ∗ ) = ( x − 5 ) ( x + 5 ) ( x + 5 ) ( x + 1 ) ​ = x − 5 x + 1 ​

Answered by kate200468 | 2024-06-10

To simplify x 2 − 25 x 2 + 6 x + 5 ​ , we can factor both the numerator and the denominator, resulting in ( x − 5 ) ( x + 5 ) ( x + 1 ) ( x + 5 ) ​ . After canceling the common factor ( x + 5 ) , the simplified expression is x − 5 x + 1 ​ , with the restriction that x  = − 5 and x  = 5 .
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Answered by Anonymous | 2024-12-23