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What is the simplified form of x minus 3 over x squared plus x minus 12 ⋅ x plus 4 over x squared plus 8x plus 16 ? 1 over the quantity x minus 4 squared 1 over the quantity x plus 3 times the quantity x minus 4 1 over the quantity x plus 4 squared 1 over the quantity x minus 3 times the quantity x plus 4

Respuesta :

i think this is the answer to the first part

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Answer:

1 over the quantity x plus 4 squared

Step-by-step explanation:

Given expression,

[tex]\frac{x-3}{x^2+x-12}.\frac{x+4}{x^2+8x+16}[/tex]

By middle term splitting,

[tex]\frac{x-3}{x^2+4x-3x-12}.\frac{x+4}{x^2+4x+4x+16}[/tex]

[tex]\frac{x-3}{x(x+4)-3(x+4)}.\frac{x+4}{x(x+4)+4(x+4)}[/tex]

[tex]\frac{x-3}{(x-3)(x+4)}.\frac{x+4}{(x+4)(x+4)}}[/tex]

[tex]=\frac{1}{x+4}.\frac{1}{x+4}[/tex]

Multiply the fractions,

[tex]=\frac{1}{(x+4)^2}[/tex]  

= 1 over the quantity x plus 4 squared

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