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Citrus2011 [14]
2 years ago
6

Solving Rational equations. LCD method. Show work. Image attached.

Mathematics
1 answer:
Dmitry [639]2 years ago
3 0

Answer:

b=1

Step-by-step explanation:

The given rational equation is

\frac{2b-5}{b-2} -2=\frac{3}{b+2}

The Least Common Denominator is (b+2)(b-2).

Multiply each term in the equation by the LCD.

(b+2)(b-2)\times \frac{2b-5}{b-2} -(b+2)(b-2)\times2=(b+2)(b-2)\times\frac{3}{b+2}

Simplify;

(b+2)\times \frac{2b-5}{1} -2(b+2)(b-2)=(b-2)\times\frac{3}{1}

(b+2)(2b-5) -2(b+2)(b-2)=3(b-2)

Expand and group similar terms

2b^2-5b+4b-10 -2(b^2-4)=3b-6

2b^2-5b+4b-10 -2b^2+8=3b-6

-b-2=3b-6

3b+b=-2+6

4b=4

b=1

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