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Question

If $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction$ then $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals$

$\frac{A}{(a x - b)^{2}} + \frac{A B}{a x - b} + \frac{B^{2}}{c x + d}$
$\frac{A}{(a x + b)^{2}} + \frac{A B}{a x - b} + \frac{B^{2}}{c x + d}$
$\frac{A}{(a x + b)^{2}} + \frac{A B}{a x + b} + \frac{B^{2}}{c x + d}$
$\frac{A}{(a x - b)^{2}} + \frac{A B}{a x + b} + \frac{B^{2}}{c x - d}$

hint Hint:

Start with the equation for which you have to find the value by substituting the known values.

The correct answer is: $fraction numerator A over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent end fraction plus fraction numerator A B over denominator a x plus b end fraction plus fraction numerator B to the power of 2 end exponent over denominator c x plus d end fraction$

Given :
$fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction$

To find $fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals$ ?

$rightwards double arrow fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis squared left parenthesis c x plus d right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis left parenthesis a x space plus b right parenthesis end fraction rightwards double arrow fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis squared left parenthesis c x plus d right parenthesis end fraction equals left curly bracket space fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction right curly bracket space cross times fraction numerator 1 over denominator a x space plus space b end fraction rightwards double arrow fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis squared left parenthesis c x plus d right parenthesis end fraction equals left curly bracket space A over left parenthesis a x plus b right parenthesis squared plus B left square bracket fraction numerator 1 over denominator left parenthesis a x space plus space b right parenthesis left parenthesis c x plus d right parenthesis end fraction right square bracket right curly bracket space W e space k n o w space t h a t space space space fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction S u b s t i t u t i n g space t h i s space v a l u e space i n space t h e space e q u a t i o n rightwards double arrow fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis squared left parenthesis c x plus d right parenthesis end fraction equals left curly bracket space A over left parenthesis a x plus b right parenthesis squared plus B left square bracket fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction right square bracket right curly bracket space M u l i t p l y i n g space a n d space o p e n i n g space t h e space b r a c k e t s rightwards double arrow fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis squared left parenthesis c x plus d right parenthesis end fraction equals space A over left parenthesis a x plus b right parenthesis squared plus fraction numerator A B over denominator a x plus b end fraction plus fraction numerator B squared over denominator c x plus d end fraction$

Related Questions to study

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parallel

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