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Please na solve it please please.​

Please na solve it please please.​-example-1
User Tarel
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2 Answers

4 votes

Answer:


\textsf{24.} \quad (1)/((x-2)(x-3))


\textsf{25.} \quad x=1, \quad x=-1

Explanation:

Question 24

Given expression:


(2)/((x-2)(x-3))+(2)/((x-1)(3-x))+(1)/((1-x)(2-x))

When adding rationals with different denominators, make the denominators the same by finding the least common denominator.

Create a common denominator by:


\textsf{Multiplying the first fraction by $(x-1)/(x-1)$}.


\textsf{Multiplying the second fraction by $(-(x-2))/(-(x-2))$}.


\textsf{Multiplying the third fraction by $(x-3)/(x-3)$}.


\implies (2)/((x-2)(x-3)) \cdot (x-1)/(x-1)+(2)/((x-1)(3-x))\cdot (-(x-2))/(-(x-2))+(1)/((1-x)(2-x))\cdot (x-3)/(x-3)


\implies (2(x-1))/((x-1)(x-2)(x-3))+(-2(x-2))/(-(x-1)(x-2)(3-x))+(x-3)/((1-x)(2-x)(x-3))


\implies (2(x-1))/((x-1)(x-2)(x-3))+(-2(x-2))/((x-1)(x-2)(-3-(-x)))+(x-3)/((-(-1+x))(-(-2+x))(x-3))


\implies (2(x-1))/((x-1)(x-2)(x-3))+(-2(x-2))/((x-1)(x-2)(x-3))+(x-3)/((x-1)(x-2)(x-3))


\textsf{Apply the fraction rule} \quad (a)/(d)+(b)/(d)+(c)/(d)=(a+b+c)/(d):


\implies (2(x-1)-2(x-2)+(x-3))/((x-1)(x-2)(x-3))

Expand the numerator:


\implies (2x-2-2x+4+x-3)/((x-1)(x-2)(x-3))


\implies (x-1)/((x-1)(x-2)(x-3))

Cancel the common factor (x - 1):


\implies (1)/((x-2)(x-3))

Question 25

Given equation:


(4x-1)(x+2)=2+7x

Expand the left side:


\implies 4x^2+7x-2=2+7x

Subtract 7x from both sides:


\implies 4x^2+7x-2-7x=2+7x-7x


\implies 4x^2-2=2

Add 2 to both sides:


\implies 4x^2-2+2=2+2


\implies 4x^2=4

Divide both sides by 4:


\implies (4x^2)/(4)=(4)/(4)


\implies x^2=1

Square root both sides:


\implies √(x^2)=√(1)


\implies x= \pm 1

Therefore, the solutions are:


x=1, \quad x=-1

User Chris Milburn
by
9.0k points
5 votes

Solution given to both questions below, they reveal the given answers.

The steps are self-explanatory, let me know if anything is unclear.

Question 24


  • \cfrac{2}{(x-2)(x-3)} +\cfrac{2}{(x-1)(3-x)}+\cfrac{1}{(1-x)(2-x)} =

  • \cfrac{2}{(x-2)(x-3)} -\cfrac{2}{(x-1)(x-3)}+\cfrac{1}{(x-1)(x-2)} =

  • \cfrac{2(x-1)}{(x-1)(x-2)(x-3)} -\cfrac{2(x-2)}{(x-1)(x-2)(x-3)}+\cfrac{x-3}{(x-1)(x-2)(x-3)} =

  • \cfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)} =

  • \cfrac{x-1}{(x-1)(x-2)(x-3)} =

  • \cfrac{1}{(x-2)(x-3)}

Question 25


  • (4x - 1)(x + 2) = 2 + 7x

  • 4x^2+8x-x-2=2+7x

  • 4x^2+7x-2=2+7x

  • 4x^2=4

  • x^2=1

  • x=√(1)

  • x=\pm1

User Taharqa
by
7.8k points

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