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Simplify completely quantity x squared minus 4 x plus 4 over quantity x squared plus 10 x plus 25 times quantity x plus 5 over quantity x squared plus 3 x minus 10.

quantity x minus 2 over quantity x plus 5
x minus 2 all over the quantity x plus 5 end quantity squared
the quantity x minus 2 end quantity squared all over x plus 5
quantity x minus 2 end quantity squared over quantity x plus 5 end quantity squared

Respuesta :

Panoyin
(x2 - 4x + 4)/(x2 + 10x + 25) • (x + 5)/(x2 + 3x - 10)
((x - 2)2)/((x + 5)2) • (x + 5)/(x + 5)(x - 2)
(x - 2)/((x + 5)2) • 1
(x - 2)/((x + 5)2)

The answer is B.

Given expression: [tex]\frac{x^2-4x+4}{x^2+10x+25}\times \frac{x+5}{x^2+3x-10}[/tex]

[tex]\mathrm{Factor}\:x^2-4x+4:\quad \left(x-2\right)^2[/tex]

[tex]\mathrm{Factor}\:x^2+3x-10:\quad \left(x-2\right)\left(x+5\right)[/tex]

[tex]\mathrm{Factor}\:x^2+10x+25:\quad \left(x+5\right)^2[/tex]

[tex]\frac{x^2-4x+4}{x^2+10x+25}\cdot \frac{x+5}{x^2+3x-10}=\frac{\left(x-2\right)^2}{\left(x+5\right)^2}\times \frac{x+5}{\left(x-2\right)\left(x+5\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factors}[/tex]

[tex]=\frac{x-2}{\left(x+5\right)^2}[/tex]

Therefore, correct option is 2nd option[tex]\frac{x-2}{\left(x+5\right)^2}.[/tex]

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