Exercise 1 Page 730

We will solve the given equation and then check the solutions.

We will solve the rational equation by cross multiplying. If a numerator or denominator contains addition or subtraction, be sure to treat each one as a parenthetical factor in the cross multiplication process.

2/x+1=4/x

Cross multiply

2x=4(x+1)

Distribute 4

2x=4x+4

LHS-4x=RHS-4x

2x-4x=4

Subtract term

-2x=4

.LHS /-2.=.RHS /-2.

x=-2

We found that x=-2 is a possible solution. Now we have to check it!

We will now check our solution to see whether it is extraneous. To do so, we will substitute x=-2 into the given equation.

2/x+1=4/x

x= -2

2/-2+1? =4/-2

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Simplify

Add terms

2/-1? =4/-2

Put minus sign in front of fraction

-2/1? =-4/2

a/1=a

-2? =-4/2

Calculate quotient

-2=-2 ✓

Since we obtained a true statement, x=-2 is a solution of the equation.