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Luda [366]
3 years ago
6

Find the quotient. h^ 6 ÷h

Mathematics
2 answers:
Arada [10]3 years ago
6 0
h^6:h=h^{6-1}=\boxed{h^5}
masha68 [24]3 years ago
6 0

Answer:

the quotient of the given expression is, h^5

Step-by-step explanation:

Use the exponent rule:

\frac{a^n}{a^m}=a^{n-m}

Given the expression:

h^6 \div h

⇒\frac{h^6}{h}

Apply the exponent rules we have;

h^{6-1}

Simplify:

h^5

therefore, the quotient of the given expression is, h^5

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<h3>The given expression can be written in the form q(x)+\frac{r(x)}{b(x)} as (2x^2-x+3)+\frac{0}{x-3} where  q(x)=2x^2-x+3 , r(x)=0 and b(x)=x-3</h3>

Step-by-step explanation:

Given rational expression is \frac{2x^3-7x^2+6x-9}{x-3}

<h3>To rewrite the given rational expression in the given form  and match their correct expressions:</h3>

Rewrite the given rational expression \frac{2x^3-7x^2+6x-9}{x-3} in the form of q(x)+\frac{r(x)}{b(x)} where q(x) is the quotient, r(x) is the remainder and b(x) is the divisor.

<h3>Now solve the given expression by using Synthetic division, we get</h3>

Since x-3 is a factor for 2x^3-7x^2+6x-9

<h3>Therefore b(x)=x-3</h3>

3_|   2     -7     6     -9

       0      6    -3      9

   ------------------------------------

      2      -1       3      0

  ------------------------------------

Therefore we have quadratic equation 2x^2-x+3=0

<h3>q(x)=2x^2-x+3</h3><h3>Remainder is 0</h3><h3>Therefore r(x)=0</h3>

Therefore we can write in the form as (2x^2-x+3)+\frac{0}{x-3}

It is in the form of q(x)+\frac{r(x)}{b(x)}

<h3>Therefore the given expression can be written in the form q(x)+\frac{r(x)}{b(x)} as (2x^2-x+3)+\frac{0}{x-3} where  q(x)=2x^2-x+3 , r(x)=0 and b(x)=x-3</h3>

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