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gladu [14]
3 years ago
11

25 point for this question:

Mathematics
1 answer:
KonstantinChe [14]3 years ago
3 0

Answer:

a=\frac{13}{11}   b =\frac{-2}{11}

Step-by-step explanation:

  • By equating coefficients on both sides of respective terms.

Given,

\frac{x-4}{x^2+7x-18} = \frac{a}{x+9} + \frac{b}{x-2}

<u>Now take  </u><u>lcm</u><u> on right hand side </u>

\frac{x-4}{x^2+7x-18} =\frac{a(x-2)+b(x+9)}{x^2+7x-18}

By equating coefficients of respective terms

x-4 = a(x-2)+b(x+9)

a+b=1  -----1 ; 9b-2a=-4  -----2

Substitute b=1-a in 2

9(1-a)-2a=-4

11a=9+4=13

a=\frac{13}{11}

As b=1-a=1- \frac{13}{11}=\frac{-2}{11}

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