Question

❊ Simplify :


`\large{ \bf{ \frac{x - 1}{ {x}^(2) - 3x + 2} + \frac{x - 2}{ {x}^(2) - 5x + 6 } + \frac{x - 5}{ {x}^(2) - 8x + 15 } }}`

`\large{ \tt{ans : \bf{ (3x - 7)/((x - 2)(x - 3)) }}}`
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- Irrelevant / Random answers will be reported!​

Answer 1

Your solution ..................

Answer 2

Need to Do :-

• To simplify the given expression .

`\red{\frak{Given}}\Bigg\{ \sf \frac{x - 1}{ {x}^(2) - 3x + 2} + \frac{x - 2}{ {x}^(2) - 5x + 6 } + \frac{x - 5}{ {x}^(2) - 8x + 15 }`

`\rule{200}4`

`\sf\longrightarrow \small \frac{x - 1}{ {x}^(2) - 3x + 2} + \frac{x - 2}{ {x}^(2) - 5x + 6 } + \frac{x - 5}{ {x}^(2) - 8x + 15 } \\\\\\\sf\longrightarrow \small ( x-1)/(x^2-x -2x +2) +( x-2)/(x^2-3x-2x+6) +( x -5)/(x^2-5x -3x + 15 ) \\\\\\\sf\longrightarrow\small ( x -1)/( x ( x - 1) -2(x-1) ) +( x-2)/(x ( x -3) -2( x -3)) +( x -5)/( x(x-5) -3( x -5) ) \\\\\\\sf\longrightarrow \small ( x -1)/( ( x-2) (x-1) ) +( x-2)/(( x -2)(x-3) ) +( x -5)/( (x-3)(x-5) ) \\\\\\\sf\longrightarrow\small ( 1)/( x-2) +( 1)/( x -3) +(1)/( x -3) \\\\\\\sf\longrightarrow \small (1)/(x-2) +(2)/(x-3) \\\\\\\sf\longrightarrow \small ( x-3 +2(x-2))/( ( x -3)(x-2) ) \\\\\\\sf\longrightarrow \small ( x - 3 +2x -4 )/( (x-3)(x-2) ) \\\\\\\sf\longrightarrow \underset{\blue{\sf Required \ Answer }}{\underbrace{\boxed{\pink{\frak{ ( 3x -7)/( ( x -2)(x-3) ) }}}}}`

`\rule{200}4`