X2-8 x-15-x2-9 x-18-x-5-x-6

The correct option is A False We can write x^2 8x+15/x^2 9x+18 as (x 3)(x 5)/(x 3)(x 6). We did this because from the R.H.S of the give equation, we can say we ...

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Byju's Answer

Standard XI

Mathematics

Inequalities Involving Modulus Function

x2-8 x+15/x2-...

Question

$\frac{x^{2} - 8 x + 15}{x^{2} - 9 x + 18} = \frac{x - 5}{x - 6}$

True

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False

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Solution

The correct option is B
False

We can write $\frac{x^{2} - 8 x + 15}{x^{2} - 9 x + 18}$ as $\frac{(x - 3) (x - 5)}{(x - 3) (x - 6)}$ . We did this because from the R.H.S of the give equation, we can say

we have to simplify/factorize the terms.

Can we write $\frac{(x - 3) (x - 5)}{(x - 3) (x - 6)} a s \frac{x - 5}{x - 6} ?$

To do that, we want $x - 3 \neq 0 o r x \neq 3$ we can write the given expression as $\frac{x - 5}{x - 6}$ if $x \neq 3$ .

But we are not given this in the question. The given statement is not true when x = 3. So we say the statement is wrong,

because we want it to be true for all the values of x.

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Similar questions

Find the value of ${lim}_{x \to 3} \frac{x^{2} - 8 x + 15}{x^{2} - 9 x + 18}$

Q. The value of

x

x^{2} - 5 x + 6 = x^{2} - 8 x + 15

Find the factors of $x^{2} + 8 x + 15$ by splitting the middle term.

Q. If

f (x) = \frac{x^{2} - b x + 36}{x^{2} - 9 x + 18}

for

x \neq 6

is continuous at

x = 6

, then value of

f (6)

Q. Factorise :
(i)

x^{2} + 7 x + 6

(ii)

x^{2} + 11 x + 18

(iii)

x^{2} + 2 x - 8

(iv)

x^{2} - 4 x - 5

(v)

x^{2} - 8 x + 12

(vi)

x^{2} - 5 x - 24

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x2−8x+15x2−9x+18=x−5x−6

$\frac{x^{2} - 8 x + 15}{x^{2} - 9 x + 18} = \frac{x - 5}{x - 6}$