(-1/3x + 9.5) + x(3/4+2.5)

Mathematics

1 answer:

Kobotan [32]3 years ago

7 0

Answer:

35x + 114

Step-by-step explanation:

(-1/3x + 9.5) + x(3/4 + 2.5)

(-1/3x + 95/10) + x(3/4 + 25/10)

(-x/3 + 5 × 19/2 × 5) + x(3/2² + 5²/2 × 5)

(-x/3 + 19/2) + x(3/2² + 5²⁻¹/2)

(2(-x) + 3 × 19/ 3 × 2) + x(3/2² + 5/2)

(-2x + 57/3 × 2) + x(3 + 2 × 5/2²)

-2x + 57/3 × 2 + x(3 + 2 × 5/2²)

-2x + 57/3 × 2 + x(13/2²)

-2x + 57/3 × 2 + x × 13/2²

-2x + 57/3 × 2 + 13x/2²

2(-2x + 57) + 3(13x)/3 × 2²

2(-2x + 57) + 3 × 13x/3 × 2²

2(-2x + 57) + 39x/3 × 2²

(-2 × 2x + 2 × 57) + 39x/3 × 2²

(-4x + 114) + 39x/3 × 2²

-4x + 114 + 39x/3 × 2²

-4x + 39x + 114/3 × 2²

35x + 114/3 × 2²

35x + 114/3 × 4

35x + 114/12

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Bingel [31]

Solution:

The rationalisation factor for $\frac{1}{ a - \sqrt{b} }$ is $a + \sqrt{b}$

So, let us apply it here.

$\frac{1}{5 - \sqrt{2} }$

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

$= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}$