How do you simplify #[(x-a)+(2a^2)/(x+a)] * [((1/x^2)-(1/a^2))] div[((x^3)-((ax^3+a^4)/(x+a)))]#?

Answer 1

#-1/(x^2a^2).#

The Exp.#=[{(x-a)(x+a)+2a^2}/(x+a)]*[(a^2-x^2)/(x^2a^2)]-:[x^3-{(a(x^3+a^3))/(x+a)}],#
#=[{(x^2-a^2)+2a^2}/(x+a)]*[{(a+x)(a-x)}/(x^2a^2)]-:[x^3-{a(x+a)(x^2-xa+a^2)}/(x+a)],#
#=(x^2+a^2)*{(a-x)/(x^2a^2)}-:[x^3-a(x^2-xa+a^2)],#
#={(x^2+a^2)(a-x)}/(x^2a^2)-:{x^3-ax^2+xa^2-a^3},#
#={(x^2+a^2)(a-x)}/(x^2a^2)-:{(x^3-a^3)-xa(x-a)},#
#={(x^2+a^2)(a-x)}/(x^2a^2)-:{(x-a)(x^2+xa+a^2)-xa(x-a)},#
#={(x^2+a^2)(a-x)}/(x^2a^2)-:{(x-a)(x^2+xa+a^2-xa)},#
#={(x^2+a^2)(a-x)}/(x^2a^2)-:{(x-a)(x^2+a^2)},#
#={(x^2+a^2)(a-x)}/(x^2a^2)xx1/{-(a-x)(x^2+a^2)},#
# rArr" The Exp.="-1/(x^2a^2).#

Enjoy Maths.!

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

#-1/(a^2x^2)#

Calling

#f_1 = x-a+(2a^2)/(x+a) = (x^2-a^2+2a^2)/(x+a)=(x^2+a^2)/(x+a)#
#f_2=1/x^2-1/a^2=(a^2-x^2)/(a^2 x^2)#
#f_3 = x^3-(ax^3+a^4)/(x+a)=(x^4+ax^3-ax^3-a^4)/(x+a)=(x^4-a^4)/(x+a)#

we have

#(f_1 f_2)/(f_3)=((x^2+a^2)/(x+a))((a^2-x^2)/(a^2 x^2))((x+a)/(x^4-a^4))=-1/(a^2x^2)#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To simplify the expression [(x-a)+(2a^2)/(x+a)] * [((1/x^2)-(1/a^2))] div[((x^3)-((ax^3+a^4)/(x+a)))], we can follow these steps:

Step 1: Simplify each term within the brackets separately.

  • Simplify (x-a) + (2a^2)/(x+a) to (x-a) + (2a^2)/(x+a).
  • Simplify (1/x^2) - (1/a^2) to (a^2 - x^2)/(x^2 * a^2).
  • Simplify (x^3 - (ax^3 + a^4)/(x+a)) to (x^3 - (ax^3 + a^4)/(x+a)).

Step 2: Combine the terms within the brackets using the distributive property.

  • Multiply (x-a) + (2a^2)/(x+a) by (a^2 - x^2)/(x^2 * a^2).
  • Divide the result by (x^3 - (ax^3 + a^4)/(x+a)).

Step 3: Simplify the resulting expression further if possible.

Please note that without specific values for the variables, it is not possible to provide a numerical answer.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7