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What is the simplified form of the quantity of x plus 7, all over the quantity of 6 − the quantity of x plus 5, all over the quantity of x plus 3?

Respuesta :

joannechan00oswszy
assuming the question looks like this: 

(x+7)/6 - (x+5)/(x+3)

multiply by (x+3):

(x+7)(x+3)/6 - (x+5)

multiply by 6:

(x+7)(x+3) - 6(x+5)

expand: 

x^2 + 10x + 21 - 6x - 30

collect like terms:

x^2 + 4x - 9

hope that helps :)

Answer:

The quantity of x squared plus 4x minus 9, all over 6 times the quantity of x plus 3

Step-by-step explanation:

Given expression,

The quantity of x plus 7, all over the quantity of 6 − the quantity of x plus 5, all over the quantity of x plus 3,

[tex]\implies \frac{x+7}{6}-\frac{x+5}{x+3}[/tex]

[tex]=\frac{(x+7)(x+3)-6(x+5)}{6(x+3)}[/tex]  ( Subtraction of fractions ),

[tex]=\frac{x(x+3)+7(x+3)-6x-30}{6(x+3)}[/tex] ( Distributive property )

[tex]=\frac{x^2+3x+7x+21-6x-30}{6(x+3)}[/tex]

[tex]=\frac{x^2+4x-9}{6(x+3)}[/tex]    ( Combine like terms ),

= The quantity of x squared plus 4x minus 9, all over 6 times the quantity of x plus 3

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