   Chapter 4.7, Problem 14PS

Chapter
Section
Textbook Problem

For problem 1-30, solve each equation. (Objective 1) 1 3 x + 4 + 6 6 x 2 + 5 x − 4 = x 2 x − 1

To determine

To Solve:

The equation 13x+4+66x2+5x4=x2x1.

Explanation

Approach:

Rational expression, a quotient obtained by division of two polynomials in form of p(x,y)q(x,y) where p(x,y) and q(x,y) are polynomials in such a way that the variables x, y do not assume values such that q(x,y)=0

If ab and cd are rational, then addition or subtraction of rational formed by making the denominator equal using LCD and perform the operation on the numerators as follows:

And,

Same algebra is for rational expression.

Calculation:

The given rational expression is 13x+4+66x2+5x4=x2x1.

Factorize each term of the equation,

13x+4+66x2+5x4=x2x113x+4+6(3x+4)(2x1)=x2x1

Restriction on the equation is that x43andx12,

The lowest common denominator of the given equation is (3x+4)(2x1).

Simplify the above equation further,

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