1.6 Rational expressions  (Page 4/6)

$\frac{3y^2-7y-6}{2y^2-3y-9}÷\frac{y^2+y-2}{2y^2+y-3}$

$\frac{6p^2+p-12}{8p^2+18p+9}÷\frac{6p^2-11p+4}{2p^2+11p-6}$

$\frac{q^2-9}{q^2+6q+9}÷\frac{q^2-2q-3}{q^2+2q-3}$

$\frac{18d^2+77d-18}{27d^2-15d+2}÷\frac{3d^2+29d-44}{9d^2-15d+4}$

$\frac{16x^2+18x-55}{32x^2-36x-11}÷\frac{2x^2+17x+30}{4x^2+25x+6}$

$\frac{144b^2-25}{72b^2-6b-10}÷\frac{18b^2-21b+5}{36b^2-18b-10}$

$\frac{16a^2-24a+9}{4a^2+17a-15}÷\frac{16a^2-9}{4a^2+11a+6}$

$\frac{22y^2+59y+10}{12y^2+28y-5}÷\frac{11y^2+46y+8}{24y^2-10y+1}$

$\frac{9x^2+3x-20}{3x^2-7x+4}÷\frac{6x^2+4x-10}{x^2-2x+1}$

$\frac{4}{x}+\frac{10}{y}$

$\frac{12}{2q}-\frac{6}{3p}$

$\frac{4}{a+1}+\frac{5}{a-3}$

$\frac{c+2}{3}-\frac{c-4}{4}$

$\frac{y+3}{y-2}+\frac{y-3}{y+1}$

$\frac{x-1}{x+1}-\frac{2x+3}{2x+1}$

$\frac{3z}{z+1}+\frac{2z+5}{z-2}$

$\frac{4p}{p+1}-\frac{p+1}{4p}$

$\frac{x}{x+1}+\frac{y}{y+1}$

$\frac{\frac{6}{y}-\frac{4}{x}}{y}$

$\frac{\frac{2}{a}+\frac{7}{b}}{b}$

$\frac{\frac{x}{4}-\frac{p}{8}}{p}$

$\frac{\frac{3}{a}+\frac{b}{6}}{\frac{2b}{3a}}$

$\frac{\frac{3}{x+1}+\frac{2}{x-1}}{\frac{x-1}{x+1}}$

$\frac{\frac{a}{b}-\frac{b}{a}}{\frac{a+b}{ab}}$

$\frac{\frac{2x}{3}+\frac{4x}{7}}{\frac{x}{2}}$

$\frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}}$

$\frac{\frac{x}{y}-\frac{y}{x}}{\frac{x}{y}+\frac{y}{x}}$

Brenda is placing tile on her bathroom floor. The area of the floor is $15x^2-8x-7$ ft ² . The area of one tile is $x^2-2x+1{\text{ft}}^2.$ To find the number of tiles needed, simplify the rational expression: $\frac{15x^2-8x-7}{x^2-2x+1}.$

The area of Sandy’s yard is $25x^2-625$ ft ² . A patch of sod has an area of $x^2-10x+25$ ft ² . Divide the two areas and simplify to find how many pieces of sod Sandy needs to cover her yard.

Aaron wants to mulch his garden. His garden is $x^2+18x+81$ ft ² . One bag of mulch covers $x^2-81$ ft ² . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.

$\frac{x^2+x-6}{x^2-2x-3}\cdot \frac{2x^2-3x-9}{x^2-x-2}÷\frac{10x^2+27x+18}{x^2+2x+1}$

$\frac{\frac{3y^2-10y+3}{3y^2+5y-2}\cdot \frac{2y^2-3y-20}{2y^2-y-15}}{y-4}$

$\frac{\frac{4a+1}{2a-3}+\frac{2a-3}{2a+3}}{\frac{4a^2+9}{a}}$

$\frac{x^2+7x+12}{x^2+x-6}÷\frac{3x^2+19x+28}{8x^2-4x-24}÷\frac{2x^2+x-3}{3x^2+4x-7}$

${\left(5-3\cdot 2\right)}^2-6$

$64÷\left(2\cdot 8\right)+14÷7$

$2\cdot 5^2+6÷2$

$5x+9=\mathrm{-11}$

$2y+4^2=64$

$9\left(y+2\right)÷3\cdot 2+1$

$3m\left(4+7\right)-m$

11

0

$\frac{5}{6}$

$\sqrt{11}$

$2^2\cdot 2^4$

$\frac{4^5}{4^3}$

${\left(\frac{a^2}{b^3}\right)}^4$

$\frac{6a^2\cdot a^0}{2a^{\mathrm{-4}}}$

$\frac{{\left(xy\right)}^4}{y^3}\cdot \frac{2}{x^5}$

$\frac{4^{\mathrm{-2}}{x}^3{y}^{\mathrm{-3}}}{2x^0}$

${\left(\frac{2x^2}{y}\right)}^{\mathrm{-2}}$

$\left(\frac{16a^3}{b^2}\right){\left(4a{b}^{\mathrm{-1}}\right)}^{\mathrm{-2}}$

Write the number in standard notation: $2.1314\times {10}^{\mathrm{-6}}$

Write the number in scientific notation: 16,340,000

$\sqrt{121}$

$\sqrt{196}$

$\sqrt{361}$

$\sqrt{75}$

$\sqrt{162}$

$\sqrt{\frac{32}{25}}$

$\sqrt{\frac{80}{81}}$

$\sqrt{\frac{49}{1250}}$

$\frac{2}{4+\sqrt{2}}$

$4\sqrt{3}+6\sqrt{3}$

$12\sqrt{5}-13\sqrt{5}$

$\sqrt[5]{\mathrm{-243}}$

$\frac{\sqrt[3]{250}}{\sqrt[3]{\mathrm{-8}}}$

$(3x^3+2x-1)+(4x^2-2x+7)$

$\left(2y+1\right)-\left(2y^2-2y-5\right)$

$(2x^2+3x-6)+(3x^2-4x+9)$

$\left(6a^2+3a+10\right)-\left(6a^2\mathrm{-3}a+5\right)$

$(k+3)(k-6)$

$(2h+1)(3h-2)$

$\left(x+1\right)\left(x^2+1\right)$

$(m-2)(m^2+2m-3)$

$\left(a+2b\right)\left(3a-b\right)$

$\left(x+y\right)\left(x-y\right)$

$81p+9pq-27p^2{q}^2$

$12x^{2}y+4x{y}^2\mathrm{-18}xy$

$88a^{3}b+4a^{2}b-144a^2$

$2x^2-9x-18$

$8a^2+30a-27$

$d^2-5d-66$

$x^2+10x+25$

$y^2-6y+9$

$4h^2-12hk+9k^2$

$361x^2-121$

$p^3+216$

$8x^3-125$

$64q^3-27p^3$

$4x{(x-1)}^{-\frac{1}{4}}+3{(x-1)}^{\frac{3}{4}}$

$3p{\left(p+3\right)}^{\frac{1}{3}}\mathrm{-8}{\left(p+3\right)}^{\frac{4}{3}}$

$4r{\left(2r-1\right)}^{-\frac{2}{3}}-5{\left(2r-1\right)}^{\frac{1}{3}}$

$\frac{x^2-x-12}{x^2-8x+16}$

$\frac{4y^2-25}{4y^2-20y+25}$

$\frac{2a^2-a-3}{2a^2-6a-8}\cdot \frac{5a^2-19a-4}{10a^2-13a-3}$

$\frac{d-4}{d^2-9}\cdot \frac{d-3}{d^2-16}$

$\frac{m^2+5m+6}{2m^2-5m-3}÷\frac{2m^2+3m-9}{4m^2-4m-3}$

$\frac{4d^2-7d-2}{6d^2-17d+10}÷\frac{8d^2+6d+1}{6d^2+7d-10}$

$\frac{10}{x}+\frac{6}{y}$

$\frac{12}{a^2+2a+1}-\frac{3}{a^2\mathrm{-1}}$

$\frac{\frac{1}{d}+\frac{2}{c}}{\frac{6c+12d}{dc}}$

$\frac{\frac{3}{x}-\frac{7}{y}}{\frac{2}{x}}$

$\mathrm{-13}$

$\sqrt{2}$

$2(x+3)-12=18$

$y{(3+3)}^2-26=10$

Write the number in standard notation: $3.1415\times {10}^6$

Write the number in scientific notation: 0.0000000212.

$\mathrm{-2}\cdot {\left(2+3\cdot 2\right)}^2+144$

$4\left(x+3\right)-\left(6x+2\right)$

$3^5\cdot 3^{\mathrm{-3}}$

${\left(\frac{2}{3}\right)}^3$

$\frac{8x^3}{{\left(2x\right)}^2}$

$\left(16y^0\right)2y^{\mathrm{-2}}$

$\sqrt{441}$

$\sqrt{490}$

$\sqrt{\frac{9x}{16}}$

$\frac{\sqrt{121b^2}}{1+\sqrt{b}}$

$6\sqrt{24}+7\sqrt{54}-12\sqrt{6}$

$\frac{\sqrt[3]{\mathrm{-8}}}{\sqrt[4]{625}}$

$(13q^3+2q^2-3)-(6q^2+5q-3)$

$\left(6p^2+2p+1\right)+\left(9p^2\mathrm{-1}\right)$

$(n-2)(n^2-4n+4)$

$(a-2b)(2a+b)$

$16x^2-81$

$y^2+12y+36$

$27c^3-1331$

$3x{(x-6)}^{-\frac{1}{4}}+2{(x-6)}^{\frac{3}{4}}$

$\frac{2z^2+7z+3}{z^2-9}\cdot \frac{4z^2-15z+9}{4z^2-1}$

$\frac{x}{y}+\frac{2}{x}$

$\frac{\frac{a}{2b}-\frac{2b}{9a}}{\frac{3a-2b}{6a}}$