Mathematics

Problem

## EXPLORATION 1 Revisiting Examples 2 and 3 1. When we cleared fractions in Example 2 we obtained the equation

5 x-1=A_{1}(x-5)+A_{2}(x+3)

. (a) Substitute

x=5

into this equation and solve for

A_{2}

. (b) Substitute

x=-3

into this equation and solve for

A_{1}

. 2. When we cleared fractions in Example 3 we obtained the equation

-x^{2}+2 x+4=A_{1}(x-2)^{2}+A_{2} x(x-2)+A_{3} x

. (a) Substitute

x=2

into this equation and solve for

A_{3}

. (b) Substitute

x=0

into this equation and solve for

A_{1}

. (c) Substitute any other value for

x

and use the values found for

A_{1}

and

A_{3}

to solve for

A_{2}