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svetlana [45]
3 years ago
14

Add or Subtract to Simplify: (x5 + x3) - (6x - x3 + 6x5)

Mathematics
1 answer:
ziro4ka [17]3 years ago
3 0

Answer:

\boxed{ \bold{   \boxed{ \sf{ - 5 {x}^{5}  + 2 {x}^{3}  - 6x}}}}

Step-by-step explanation:

\sf{( {x}^{5}  +  {x}^{3} ) - (6x -  {x}^{3}  + 6 {x}^{5}) }

When there is a ( - ) in front of an expression in parentheses , change the sign of each term.

Also, remove the parentheses

⇒\sf{ {x}^{5}  +  {x}^{3}  - 6x +  {x}^{3}  - 6 {x}^{5} }

Collect like terms

⇒\sf{ {x}^{5}  - 6 {x}^{5}  +  {x}^{3}  +  {x}^{3}  - 6x}

⇒\sf{ - 5 {x}^{5}  + 2 {x}^{3}  - 6x}

Hope I helped!

Best regards!!

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The correct graph is shown in attached figure.

Step-by-step explanation:

Considering the function

f\left(x\right)=\frac{1}{x\left(x+4\right)}

\mathrm{Domain\:of\:}\:\frac{1}{x\left(x+4\right)}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x

\mathrm{Range\:of\:}\frac{1}{x\left(x+4\right)}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:-\frac{1}{4}\quad \mathrm{or}\quad \:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{1}{4}]\cup \left(0,\:\infty \:\right)\end{bmatrix}

\mathrm{Axis\:interception\:points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{None}

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So, the correct graph is shown in attached figure.

Therefore, the correct option is D.

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f\left(x\right)=\frac{1}{x\left(x+4\right)} is the correct option.

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