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Solve the following rational equations. SHOW YOUR COMPLETE SOLUTION. (Follow the steps

in solving rational equation in your module.)(3points each)

6. Solve for x. 4



2−8+12

=



−2

+

1

−6

7. Solve for x. 5

+2

=

1

−4

8. Solve for x. − 8 = −

15

​

Solve The Following Rational Equations SHOW YOUR COMPLETE SOLUTION Follow The Steps In Solving Rational Equation In Your Module3points Each6 Solve For X 4281221 class=

Sagot :

Dekzipalidn

Answer:

6.

[tex] \frac{4}{x {}^{2} - 8x + 12 }= \frac{x}{x - 2} + \frac{1}{x - 6} \\ \frac{4}{(x - 6)(x - 2)} = \frac{x}{x - 2} + \frac{1}{x - 6} \\ \frac{4(x - 6)(x - 2)}{(x - 6)(x - 2)} = \frac{x(x - 6)(x - 2)}{x - 2} + \frac{1(x - 6)(x - 2)}{x - 6} \\ 4 = x(x - 6) +(x - 2) \\ 4 = x {}^{2} - 6x + x - 2 \\ x {}^{2} - 5x - 6 = 0 \\ (x - 6)(x + 1) = 0 \\ \\ x = 6 \: \: \: \: \: \: \: \: \: \:x = - 1[/tex]

7.

[tex] \frac{5}{x + 2} = \frac{1}{x - 4} \\ \frac{5(x + 2)(x - 4)}{x + 2} = \frac{1(x + 2)(x - 4)}{x - 4} \\5x - 20 = x +2 \\ 4x = 22 \\ x = \frac{11}{2} [/tex]

8.

[tex]x - 8 = - \frac{15}{x} \\ x - 8(x) = - \frac{15(x)}{x} \\ x {}^{2} - 8x = - 15 \\ x {}^{2} - 8x + 15 = 0 \\ (x - 5)(x - 3) = 0 \\ \\ x = 5 \: \: \: \: \: \: \: \: \: \: x = 3[/tex]