Simplify 7x-x2-9x-14-4-x-7-

Simplifying the given expression:=7x/x^2 9x+14 4/x 70ex0ex=7x/x^2 7x 2x+14 4/x 70ex0ex=7x/x(x 7) 2(x 7) 4/x 70ex0ex=7x/(x 7)(x 2) 4/x 70ex0ex=7x 4(x 2)/(x 7)(x ...

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Byju's Answer

Standard XII

Mathematics

Theorems for Continuity

Simplify 7x/x...

Question

Simplify $\frac{7 x}{x^{2} - 9 x + 14} - \frac{4}{x - 7}$ .

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Solution

Simplifying the given expression:
$= \frac{7 x}{x^{2} - 9 x + 14} - \frac{4}{x - 7} = \frac{7 x}{x^{2} - 7 x - 2 x + 14} - \frac{4}{x - 7} = \frac{7 x}{x (x - 7) - 2 (x - 7)} - \frac{4}{x - 7} = \frac{7 x}{(x - 7) (x - 2)} - \frac{4}{x - 7} = \frac{7 x - 4 (x - 2)}{(x - 7) (x - 2)} = \frac{7 x - 4 x + 8}{(x - 7) (x - 2)} = \frac{3 x + 8}{(x - 7) (x - 2)}$
Hence, the simplified form is $\frac{3 x + 8}{(x - 7) (x - 2)}$ .

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Simplify 7xx2-9x+14-4x-7.

Simplifying the given expression:=7xx2-9x+14-4x-7=7xx2-7x-2x+14-4x-7=7xx(x-7)-2(x-7)-4x-7=7x(x-7)(x-2)-4x-7=7x-4(x-2)(x-7)(x-2)=7x-4x+8(x-7)(x-2)=3x+8(x-7)(x-2)Hence, the simplified form is 3x+8(x-7)(x-2).

Simplify $\frac{7 x}{x^{2} - 9 x + 14} - \frac{4}{x - 7}$ .