Question

Express x²-12x+32/x²-7x + 12 in its lowest terms.​

Answer 1

Answer:

$\huge\bf\underline\red{AnSweR:}$

Here,

$p(x) = {x}^{2} - 12x + 32$

$= (x - 4)(x - 8)$

$q(x) = {x}^{2} - 7x + 12$

$= (x - 3)(x - 4)$

G.c.d.

$p(x) \:or \: q(x) = (x - y)$

The Given Expression is

$\frac{(x - 4)(x - 8)}{(x - 3)(x - 4)}$

is cancelling (x-4),

We get the Rational Expression in its lowest Form as

$= \frac{x - 8}{x - 3}$

Hope it will be helpful :)

Answer 2

Step-by-step explanation:

${x}^{2} - 12x + 32 \\ = {x}^{2} - 8x - 4x + 32 \\ = x(x - 8) - 4(x - 8) \\ = (x - 8)(x - 4)$ [ By middle-term factorisation ]

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${x}^{2} - 7x + 12 \\ = {x}^{2} - 4x - 3x + 12 \\ = x(x - 4) - 3(x - 4) \\ = (x - 4)(x - 3)$ [ By middle-term factorisation ]

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$\frac{ {x}^{2} - 12x + 32}{ {x}^{2} - 7x + 12 } \\ = \frac{(x - 8)(x - 4)}{(x - 4)(x - 3)} \\ = \frac{(x - 8)}{(x - 3)}$ [ On cancelling (x-4) from both the numerator and denominator ]

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