BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 76RE
To determine

To find the real solutions of equation 1x+2x1=3 .

Expert Solution

Answer to Problem 76RE

The solution is x=±13 .

Explanation of Solution

Given information:

  1x+2x1=3

Formula used:

Properties of fractions:- AC+BC=A+BC .

Distributive property:- a(b+c)=ab+ac

Calculations:

  =1x+2(x1)=3

  =(x1)x(x1)+2xx(x1)=3 (Re-write in LCD form)

  =x1+2xx(x1)=3=3x1x(x+1)=3

  =3x1=3(x)(x+1) (by cross - multiplying)

  =3x1=3x(x+1)=3x1=3x(x)+3x(1)=3x1=3x2+3x

  =3x13x23x=0

  =13x2=0 (Subtracting like terms)

  =13x2+1=0+1 (Adding 1 on both the sides)

  =3x2=1

  =3x23=13 (Dividing by (-3) on both the sides)

  =x2=13

  =x=±13 (Taking under-root both the sides)

The solution of the equation x=±13 .

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